rss_2.0Moroccan Journal of Pure and Applied Analysis FeedSciendo RSS Feed for Moroccan Journal of Pure and Applied Analysishttps://sciendo.com/journal/MJPAAhttps://www.sciendo.comMoroccan Journal of Pure and Applied Analysis 's Coverhttps://sciendo-parsed-data-feed.s3.eu-central-1.amazonaws.com/62929afb27619c39e443076d/cover-image.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20220627T215031Z&X-Amz-SignedHeaders=host&X-Amz-Expires=604800&X-Amz-Credential=AKIA6AP2G7AKP25APDM2%2F20220627%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Signature=8965ee8cd5eb409bc6b45205b61f9f203f29288ac3467cebec76a2ecc586a3fb200300CQ *-algebras of measurable operatorshttps://sciendo.com/article/10.2478/mjpaa-2022-0019<abstract> <title style='display:none'>Abstract</title> <p>We study, from a quite general point of view, a CQ*-algebra (X, 𝖀<sub>0</sub>) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative <italic>L</italic><sup>2</sup>-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, 𝖀<sub>0</sub>) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative <italic>L</italic><sup>2</sup>-spaces.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equationhttps://sciendo.com/article/10.2478/mjpaa-2022-0018<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we are interested in some theoretical and numerical studies of a special case of a degenerate nonlinear Schrödinger equation namely the so-called Gross-Pitaevskii Equation(GPE). More precisely, we will treat in a first time the well-posedness of GPE model with a degeneracy occurring in the interior of the space variable domain, i.e ∃<italic>x</italic><sub>0</sub> ∈ (0, <italic>L</italic>), <italic>s</italic>. <italic>t k</italic>(<italic>x</italic><sub>0</sub>) = 0, where <italic>k</italic> stands for the diffusion coefficient and <italic>L</italic> is a positive constant. Thereafter, we will focus ourselves on some numerical simulations showing the influence of a different parameters, especially the interior degeneracy, on the behavior of the wave solution corresponding to our model in a special case of the function <italic>k</italic> namely <italic>k</italic>(<italic>x</italic>) = |<italic>x</italic> − <italic>x</italic><sub>0</sub>| <sup>α</sup>, <italic>α</italic> ∈ (0, 1).</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Existence and multiplicity results for fractional ()-Laplacian Dirichlet problemhttps://sciendo.com/article/10.2478/mjpaa-2022-0011<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we study a class of fractional <italic>p</italic>(<italic>x</italic>)-Laplacian Dirichlet problems in a bounded domain with Lipschitz boundary. Using variational methods, we prove in different situations the existence and multiplicity of solutions.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Renormalized solutions for a (·)-Laplacian equation with Neumann nonhomogeneous boundary condition involving diffuse measure data and variable exponenthttps://sciendo.com/article/10.2478/mjpaa-2022-0012<abstract> <title style='display:none'>Abstract</title> <p>In this paper we prove the existence of at least one renormalized solution for the p(x)-Laplacian equation associated with a maximal monotone operator and Radon measure data. The functional setting involves Sobolev spaces with variable exponent <italic>W</italic><sup>1,</sup><italic><sup>p</sup></italic><sup>(</sup>·<sup>)</sup>(Ω).</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Existence of solutions for 4p-order PDEShttps://sciendo.com/article/10.2478/mjpaa-2022-0013<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we study the following nonlinear eigenvalue problem: <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0013_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>p</mml:mi></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mi>m</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>i</mml:mi><mml:mi>n</mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mo>…</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow> </mml:mrow></mml:mrow></mml:math> <tex-math>\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\Omega ,} \cr {u = \Delta u = \ldots {\Delta ^{2p - 1}}u = 0\,\,\,\,on\,\,\partial \Omega .} \cr } } \right.</tex-math> </alternatives> </disp-formula> Where Ω is a bounded domain in ℝ<italic><sup>N</sup></italic> with smooth boundary ∂ Ω, <italic>N ≥</italic> 1, <italic>p</italic> ∈ ℕ<sup>*</sup>, <italic>m</italic> ∈ <italic>L<sup>∞</sup></italic> (Ω), <italic>µ</italic>{<italic>x</italic> ∈ Ω: <italic>m</italic>(<italic>x</italic>) &gt; 0} ≠ 0, and Δ<sup>2</sup><italic><sup>p</sup>u</italic> := Δ (Δ...(Δ<italic>u</italic>)), 2<italic>p</italic> times the operator Δ.</p> <p>Using the Szulkin’s theorem, we establish the existence of at least one non decreasing sequence of nonnegative eigenvalues.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Bayesian Inference for SIR Epidemic Model with dependent parametershttps://sciendo.com/article/10.2478/mjpaa-2022-0017<abstract> <title style='display:none'>Abstract</title> <p>This paper is concerned with the Bayesian inference for the dependent parameters of stochastic SIR epidemic model in a closed population. The estimation framework involves the introduction of <italic>m</italic> − 1 latent data between every pair of observations. Kibble’s bivariate gamma distribution is considered as a good candidate prior density of parameters, they give an appropriate frame to model the dependence between the parameters. A Markov chain Monte Carlo methods are then used to sample the posterior distribution of the model parameters. Simulated datasets are used to illustrate the proposed methodology.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Least energy sign-changing solutions for a nonlocal anisotropic Kirchhoff type equationhttps://sciendo.com/article/10.2478/mjpaa-2022-0015<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we investigate the existence of sign-changing solutions for the following class of fractional Kirchhoff type equations with potential <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0015_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:msubsup><mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mi>u</mml:mi> <mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mi>α</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mi>α</mml:mi></mml:msup><mml:mi>u</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:mi>u</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>V</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>∈</mml:mo><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mi>m</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math> <tex-math>\left( {1 + b\left[ u \right]_\alpha ^2} \right)\left( {{{\left( { - {\Delta _x}} \right)}^\alpha }u - {\Delta _y}u} \right) + V\left( {x,y} \right)u = f\left( {x,y,u} \right),\left( {x,y} \right) \in {\mathbb{R}^N} = {\mathbb{R}^n} \times {\mathbb{R}^m},</tex-math> </alternatives> </disp-formula> where <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0015_eq_002.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mrow><mml:mo>[</mml:mo> <mml:mi>u</mml:mi> <mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mi>α</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mrow><mml:mo>∫</mml:mo><mml:mrow><mml:msub><mml:mrow/><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mi>N</mml:mi></mml:msup></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mfrac><mml:mi>α</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:msup><mml:mi>u</mml:mi></mml:mrow> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mrow><mml:msub><mml:mrow><mml:mo>∇</mml:mo></mml:mrow><mml:mi>y</mml:mi></mml:msub><mml:mi>u</mml:mi></mml:mrow> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>x</mml:mi><mml:mi>d</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math> <tex-math>{\left[ u \right]_\alpha } = {\left( {\int {_{{\mathbb{R}^N}}\left( {{{\left| {{{\left( { - {\Delta _x}} \right)}^{{\alpha \over 2}}}u} \right|}^2} + {{\left| {{\nabla _y}u} \right|}^2}} \right)dxdy} } \right)^{{1 \over 2}}}</tex-math> </alternatives> </inline-formula>. Based on variational approach and a variant of the quantitative strain lemma, for each <italic>b &gt;</italic> 0, we show the existence of a least energy nodal solution <italic>u<sub>b</sub></italic>. In addition, a convergence property of <italic>u<sub>b</sub></italic> as <italic>b</italic> ↘ 0 is established.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Further results on strictly Lipschitz summing operatorshttps://sciendo.com/article/10.2478/mjpaa-2022-0014<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to give some new characterizations of strictly Lipschitz <italic>p</italic>-summing operators. These operators have been introduced in order to improve the Lipschitz <italic>p</italic>-summing operators. Therefore, we adapt this definition for constructing other classes of Lipschitz mappings which are called strictly Lipschitz <italic>p</italic>-nuclear and strictly Lipschitz (<italic>p</italic>, <italic>r</italic>, <italic>s</italic>)-summing operators. Some interesting properties and factorization results are obtained for these new classes.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Steklov problems for the −Laplace operator involving -normhttps://sciendo.com/article/10.2478/mjpaa-2022-0016<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we are concerned with the study of the spectrum for the nonlinear Steklov problem of the form <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2022-0016_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mi>p</mml:mi></mml:msub><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mtext>in</mml:mtext><mml:mi> </mml:mi><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mrow><mml:mo>∇</mml:mo><mml:mi>u</mml:mi></mml:mrow> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:mi>v</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:msubsup><mml:mrow><mml:mrow><mml:mrow><mml:mo>‖</mml:mo> <mml:mi>u</mml:mi> <mml:mo>‖</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mtext>on</mml:mtext><mml:mi> </mml:mi><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow> </mml:mrow></mml:mrow></mml:math> <tex-math>\left\{ {\matrix{{{\Delta _p}u = {{\left| u \right|}^{p - 2}}u} \hfill &amp; {{\rm{in}}\,\Omega ,} \hfill \cr {{{\left| {\nabla u} \right|}^{p - 2}}{{\partial u} \over {\partial v}} = \lambda \left\| u \right\|_{q,\partial \Omega }^{p - q}{{\left| u \right|}^{q - 2}}u} \hfill &amp; {{\rm{on}}\,\partial \Omega ,} \hfill \cr } } \right.</tex-math> </alternatives> </disp-formula> where Ω is a smooth bounded domain in ℝ<italic><sup>N</sup></italic>(<italic>N</italic> ≥ 1), λ is a real number which plays the role of eigenvalue and the unknowns <italic>u</italic> ∈ <italic>W</italic><sup>1,</sup><italic><sup>p</sup></italic>(Ω). Using the Ljusterneck-Shnirelmann theory on <italic>C</italic><sup>1</sup> manifold and Sobolev trace embedding we prove the existence of an increasing sequence positive of eigenvalues (λ<italic><sub>k</sub></italic>)<italic><sub>k</sub></italic><sub>≥1</sub>, for the above problem. We then establish that the first eigenvalue is simple and isolated.</p> </abstract>ARTICLE2022-05-28T00:00:00.000+00:00Generalized Canavati Fractional Ostrowski, Opial and Grüss type inequalities for Banach algebra valued functionshttps://sciendo.com/article/10.2478/mjpaa-2022-0010<abstract> <title style='display:none'>Abstract</title> <p>Using generalized Canavati fractional left and right vectorial Taylor formulae we establish mixed fractional Ostrowski, Opial and Grüss type inequalities involving several Banach algebra valued functions. The estimates are with respect to all norms ‖ · ‖ <italic><sub>p</sub></italic>, 1 ≤ <italic>p</italic> ≤ ∞. We provide also applications.</p> </abstract>ARTICLE2022-01-13T00:00:00.000+00:00Entropy Stable Discontinuous Galerkin Finite Element Method with Multi-Dimensional Slope Limitation for Euler Equationshttps://sciendo.com/article/10.2478/mjpaa-2022-0009<abstract> <title style='display:none'>Abstract</title> <p>We present an entropy stable Discontinuous Galerkin (DG) finite element method to approximate systems of 2-dimensional symmetrizable conservation laws on unstructured grids. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. The method is designed to work on structured as well as on unstructured meshes. As solutions of hyperbolic conservation laws can develop discontinuities (shocks) in finite time, we include a multidimensional slope limitation step to suppress spurious oscillations in the vicinity of shocks. The numerical scheme has two steps: the first step is a finite element calculation which includes calculations of fluxes across the edges of the elements using 1-D entropy stable solver. The second step is a procedure of stabilization through a truly multi-dimensional slope limiter. We compared the Entropy Stable Scheme (ESS) versus Roe’s solvers associated with entropy corrections and Osher’s solver. The method is illustrated by computing solution of the two stationary problems: a regular shock reflection problem and a 2-D flow around a double ellipse at high Mach number.</p> </abstract>ARTICLE2022-01-13T00:00:00.000+00:00An efficient algorithm for solving the conformable time-space fractional telegraph equationshttps://sciendo.com/article/10.2478/mjpaa-2021-0028<abstract> <title style='display:none'>Abstract</title> <p>In this paper, an efficient algorithm is proposed for solving one dimensional time-space-fractional telegraph equations. The fractional derivatives are described in the conformable sense. This algorithm is based on shifted Chebyshev polynomials of the fourth kind. The time-space fractional telegraph equations is reduced to a linear system of second order differential equations and the Newmark’s method is applied to solve this system. Finally, some numerical examples are presented to confirm the reliability and effectiveness of this algorithm.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Some fixed point theorems of rational type contraction in -metric spaceshttps://sciendo.com/article/10.2478/mjpaa-2021-0023<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we prove some common fixed point theorems satisfying contractive type mapping in the setting of <italic>b</italic>-metric spaces. The presented theorem is an extension the results of M. Sarwar and M. U. Rahman [23] as well as a generalization of many well-known results in the literature through the context of b-metric spaces. Also, we present a few examples to illustrate the validity of the results obtained in the paper. Finally, results are applied to find the solution for an integral equation.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00Jacobson’s Lemma in the ring of quaternionic linear operatorshttps://sciendo.com/article/10.2478/mjpaa-2021-0031<abstract> <title style='display:none'>Abstract</title> <p>In the present paper, we study the Jacobson’s Lemma in the unital ring of all bounded right linear operators ℬ<italic><sub>R</sub></italic>(<italic>X</italic>) acting on a two-sided quaternionic Banach space <italic>X</italic>. In particular, let <italic>A</italic>, <italic>B</italic> ∈ ℬ<italic><sub>R</sub></italic>(<italic>X</italic>) and let <italic>q</italic> ∈ ℍ \ {0}, we prove that <italic>w</italic>(<italic>AB</italic>) \ {0} = <italic>w</italic>(<italic>BA</italic>) \ {0} where <italic>w</italic> belongs to the spherical spectrum, the spherical approximate point spectrum, the right spherical spectrum, the left spherical spectrum, the spherical point spectrum, the spherical residual spectrum and the spherical continuous spectrum. We also prove that the range of (<italic>AB</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>AB</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is closed if and only if (<italic>BA</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>BA</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> has closed range. Finally, we show that (<italic>AB</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>AB</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is Drazin invertible if and only if (<italic>BA</italic>)<sup>2</sup> − 2Re(<italic>q</italic>)<italic>BA</italic> + |<italic>q</italic>|<sup>2</sup><italic>I</italic> is.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Certain Classes of Analytic Functions Associated With -Analogue of -Valent Cătaş Operatorhttps://sciendo.com/article/10.2478/mjpaa-2021-0029<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we investigate several interesting properties for certain class of analytic functions defined by q-analogue of p-valent Cătaş operator. All our results are sharp.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00On a Class of Caputo Time Fractional Problems with Boundary Integral Conditionshttps://sciendo.com/article/10.2478/mjpaa-2021-0027<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to work out the solvability of a class of Caputo time fractional problems with boundary integral conditions. A generalized formula of integration is demonstrated and applied to establish the a priori estimate of the solution, then we prove the existence which is based on the range density of the operator associated with the problem.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Integral geometry on discrete matriceshttps://sciendo.com/article/10.2478/mjpaa-2021-0024<abstract> <title style='display:none'>Abstract</title> <p>In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00Some results about Lipschitz -Nuclear Operatorshttps://sciendo.com/article/10.2478/mjpaa-2021-0025<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to study the onto isometries of the space of strongly Lipschitz <italic>p</italic>-nuclear operators, introduced by D. Chen and B. Zheng (Nonlinear Anal.,75, 2012). We give some new results about such isometrics and we focus, in particular, on the case <italic>F</italic> = ℓ<sub><italic>p</italic>*</sub>.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00On the generalized fractional Laplace transformhttps://sciendo.com/article/10.2478/mjpaa-2021-0030<abstract> <title style='display:none'>Abstract</title> <p>In the present paper a generalization of the Laplace transform is introduced and studied. Its inversion formula is also obtained. As an application, we obtain the generalized fractional Laplace transform of a general class of functions and a product of the Fox’s <italic>H</italic>- function and general class of functions. The results obtained are of general nature and capable of yielding a large number of known or new results as special cases. For illustration, some special cases involving important special functions are mentioned.</p> </abstract>ARTICLE2021-04-30T00:00:00.000+00:00Integral inequalities via harmonically -convexityhttps://sciendo.com/article/10.2478/mjpaa-2021-0026<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic <italic>h</italic>-preinvex functions involving Euler’s beta and hypergeometric functions. The obtained results are mainly based on the identity given by M. A. Noor, K. I. Noor and S. Iftikhar in [17].</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00en-us-1