rss_2.0Sciendo RSS Feed for General Mathematicshttps://sciendo.com/journal/GMhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/65617d4fc4f7d26fa6b5540d/cover-image.jpghttps://sciendo.com/journal/GM140216https://sciendo.com/article/10.2478/gm-2022-0002<abstract> <title style='display:none'>Abstract</title> <p>In this paper, some common fixed point theorems for pairs of subcompatible and reciprocally continuous mappings or compatible and subsequentially continuous mappings satisfying integral type are obtained. Our results improve several results especially the results of [<xref ref-type="bibr" rid="j_gm-2022-0002_ref_003">3</xref>], Pathak et al. [<xref ref-type="bibr" rid="j_gm-2022-0002_ref_013">13</xref>], Djoudi and Aliouche [<xref ref-type="bibr" rid="j_gm-2022-0002_ref_006">6</xref>], Mbarki [<xref ref-type="bibr" rid="j_gm-2022-0002_ref_010">10</xref>] and others.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00022023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0001<abstract> <title style='display:none'>Abstract</title> <p>In this investigation, we introduce a new <italic>q</italic>-differential operator that generalizes the well-known Opoola differential operator. Using the operator, we define a family of <italic>q</italic>-bounded turning functions. The new class is denoted by ℛ<italic>_qⁿ</italic> (<italic>µ, β, τ </italic>; <italic>λ</italic>). Afterwards, inclusion, characterisation, growth, distortion, covering, linear combination and neighborhood properties of functions <italic>f ∈ </italic>ℛ<italic>_qⁿ</italic> (<italic>µ, β, τ </italic>; <italic>λ</italic>) are presented.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00012023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0006<abstract> <title style='display:none'>Abstract</title> <p>In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are <italic>h</italic>-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00062023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0004<abstract> <title style='display:none'>Abstract</title> <p>The aim of this paper is to generalize the convexity preserving properties of sets by direct and inverse images initially stated for set-valued ratios of affine functions to a broader class of fractional type set-valued functions which strictly includes the first one.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00042023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0003<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce a new class of generalized convex functions called (<italic>h, r</italic>)-preinvex functions, and establish some new Hermite-Hadamard type inequalities under (<italic>h, r</italic>)-preinvexity.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00032023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0005<abstract> <title style='display:none'>Abstract</title> <p>This paper consists of Hankel results of <italic>ω</italic>-order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that <italic>ω</italic>-order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of <italic>T </italic>(<italic>t</italic>) to a <italic>C</italic>₀-semigroup ̂<italic>T</italic>(<italic>t</italic>) on a space ̂<italic>X </italic>containing <italic>X </italic>isometrically bounded. The space is constructed in such a way that the spectrum of the generator <italic>A </italic>of <italic>T </italic>(<italic>t</italic>) coincides with the spectrum of the generator <italic>Â </italic>of ̂<italic>T</italic>(<italic>t</italic>) and the approximate point spectrum of <italic>A </italic>coincides with the point spectrum of <italic>Â</italic>.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00052023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0009<abstract> <title style='display:none'>Abstract</title> <p>We introduce a new iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of multivalued quasi-nonexpansive. Futhermore, we applied our main result for finding a common solution of convex minimization problem and fixed points problem. Essentially a new approach for finding solutions of equilibrium problems and fixed point problems whith set-valued operators is provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00092023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0008<abstract> <title style='display:none'>Abstract</title> <p>In this paper, unique common fixed point theorems for pairs of subcompatible and reciprocally continuous mappings or compatible and subsequentially continuous mappings are obtained. This unique common fixed point is guaranteed under a new concept named a weak altering distance function. Our theorems improve some results especially the ones of [<xref ref-type="bibr" rid="j_gm-2022-0008_ref_002">2</xref>].</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00082023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0007<abstract> <title style='display:none'>Abstract</title> <p>For a continuous and positive function <italic>w </italic>(<italic>λ</italic>), <italic>λ &gt; </italic>0 and <italic>µ </italic>a positive measure on (0, <italic><bold>∞</bold></italic>) we consider the following <italic>integral transform</italic> <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2022-0007_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mstyle><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>∞</mml:mi></mml:msubsup><mml:mrow><mml:mi>w</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>λ</mml:mi><mml:mo>+</mml:mo><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mi>d</mml:mi><mml:mi>μ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>λ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math> <tex-math>\mathcal{D}\left( {w,\mu } \right)\left( T \right): = \int_0^\infty {w\left( \lambda \right){{\left( {\lambda + T} \right)}^{ - 1}}d\mu \left( \lambda \right)} ,</tex-math> </alternatives> </disp-formula> where the integral is assumed to exist for <italic>T </italic>a positive operator on a complex Hilbert space <italic>H</italic>.</p> <p>We show among others that, if <italic>B, A &gt; </italic>0, then <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2022-0007_eq_002.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>−</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>=</mml:mo><mml:mstyle><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mi>∞</mml:mi></mml:msubsup><mml:mrow><mml:mi>w</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mstyle><mml:mrow><mml:msubsup><mml:mo>∫</mml:mo><mml:mn>0</mml:mn><mml:mn>1</mml:mn></mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>λ</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>t</mml:mi><mml:mi>A</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>B</mml:mi><mml:mo>−</mml:mo><mml:mi>A</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:mstyle></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>μ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>λ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:mrow></mml:mstyle></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math> <tex-math>\matrix{{\left[{\mathcal{D}\left({w,\mu}\right)\left(A\right)-\mathcal{D}\left({w,\mu}\right)\left(B\right)}\right]\left({B-A}\right)}\cr{=\int_0^\infty{w\left(\lambda\right)\left({\int_0^1{{{\left[{\lambda+\left({1-t}\right)B+tA{)^{-1}}\left({B-A}\right)}\right]}^2}dt}}\right)d\mu\left(\lambda\right).}}\cr}</tex-math> </alternatives> </disp-formula> We also provide some sufficient conditions for the operators <italic>A, B &gt; </italic>0 such that the inequality <disp-formula> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2022-0007_eq_003.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>B</mml:mi><mml:mo>+</mml:mo><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>A</mml:mi><mml:mo>≥</mml:mo><mml:mi>A</mml:mi><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>B</mml:mi><mml:mi>𝒟</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>w</mml:mi><mml:mo>,</mml:mo><mml:mi>μ</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>B</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> <tex-math>\mathcal{D}\left({w,\mu}\right)\left(A\right)B+\mathcal{D}\left({w,\mu}\right)\left(B\right)A{\ge}A\mathcal{D}\left({w,\mu}\right)\left(A\right)+B\mathcal{D}\left({w,\mu}\right)\left(B\right)</tex-math> </alternatives> </disp-formula> holds. Some examples for power and logarithmic functions are also provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00072023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0003<abstract> <title style='display:none'>Abstract</title> <p>In 2013, Azadifar et al. [<xref ref-type="bibr" rid="j_gm-2023-0003_ref_003">3</xref>] established fixed point result in integral type contraction in modular metric space and 2020, Chaira et al.[<xref ref-type="bibr" rid="j_gm-2023-0003_ref_011">11</xref>] established some extensions of Fixed Point Theorems for Weak-Contraction Mapping in Partially Ordered Modular Metric Spaces.</p> <p>In this paper we have established some common fixed point results in integral type contractions in modular and convex modular metric spaces.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00032023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0002<abstract> <title style='display:none'>Abstract</title> <p>In this scientific research note, certain necessary-basic information in relation to some types of the operators specified by fractional calculus of arbitrary order will be firstly introduced, various argument properties of certain analytic functions specified by those fractional-order type operators will be then determined, and a number of special consequences of those extensive properties will be also pointed out.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00022023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0006<abstract> <title style='display:none'>Abstract</title> <p>In this article we present a method to get upper bound for some integrals. The method is in connection with on a generalized trapezoidal quadrature formula. Applications for upper bounds of the elliptical integral of the first kind are presented. We compare these bounds with some previous results from the literature.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00062023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0005<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we prove a new coincidence and common fixed point theorem of hybrid mappings using the <italic>C</italic>-class function and <italic>T </italic>-weak commutativity. Finally, we give an example to illustrate our result.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00052023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0004<abstract> <title style='display:none'>Abstract</title> <p>The purpose of this paper is to establish convergence and stability of Jungck -modified three-step iterations for three nonself mappings in a Banach space. The results obtained in this paper extend and improve the recent ones announced by Khan et al., Olatinwo, Hussain et al. and many papers.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00042023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0001<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we determine properties of the coefficients of the integral operator <italic>G_α</italic>_{1, <italic>α</italic>2},...,<italic>αn</italic>,<italic>β</italic> . We want to see if some results obtained on the interior unit disk can be extended on the exterior unit disk, so we make use of the usual transformation <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2023-0001_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>g</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>z</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math> <tex-math>g\left( z \right) = {1 \over {f\left( {{1 \over z}} \right)}}</tex-math> </alternatives> </inline-formula>.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00012023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2023-0007<abstract> <title style='display:none'>Abstract</title> <p>To approximate a function, some simpler functions are used: simpler as definitory structure (formula) and also as regularity, continuity and/or smoothness.</p> <p>Any Lipschitz function is a uniformly continuous function, but conversely it not always true. We add to the usual examples some other, especially of the class of differentiable functions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2023-00072023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0013<abstract> <title style='display:none'>Abstract</title> <p>V. Gupta introduced recently the Rathore type operators <italic>R_n,c</italic>. For them we obtain Voronovskaja type results. We extend the classical Szász-Mirakjan operator and compare the extension with <italic>R_n,c</italic>.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00132023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0010<abstract> <title style='display:none'>Abstract</title> <p>In this paper we introduce a novel extension of generalized Bézier operators by replacing the sample values <inline-formula> <alternatives> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_gm-2022-0010_eq_001.png"/> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mi>k</mml:mi><mml:mi>n</mml:mi></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> <tex-math>f\left({{k\overn}}\right)</tex-math> </alternatives> </inline-formula> with the wavelet expansion of the function <italic>f. </italic>Using the compactly supported Daubechies wavelets, we construct a wavelet type extension of the generalized Bézier operators defined by Gupta [<xref ref-type="bibr" rid="j_gm-2022-0010_ref_007">7</xref>]. Moreover, we investigate some properties of these operators in some function spaces.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00102023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0011<abstract> <title style='display:none'>Abstract</title> <p>In this article, two unique common fixed point theorems for four self-maps on a metric-like space by using the concept of occasionally weakly biased maps of type (𝒜) are proved. Our results represent an improvement and extension of some fixed point findings. We justify our results by giving two appropriate examples.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00112023-11-24T00:00:00.000+00:00https://sciendo.com/article/10.2478/gm-2022-0012<abstract> <title style='display:none'>Abstract</title> <p>The composition ℱ_{<italic>n </italic>}of Rathore and Gamma operators was considered in the literature. We introduce a generalization of ℱ_{<italic>n</italic>}. For it we determine the eigenstructure and establish the corresponding Voronovskaja type formula.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/gm-2022-00122023-11-24T00:00:00.000+00:00en-us-1