rss_2.0General Mathematics FeedSciendo RSS Feed for General Mathematics Mathematics Feed certain classes of analytic functions of Complex order defined by Erdelyi-Kober integral operator<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we consider new subclasses 𝔗𝔖<italic><sub>n</sub></italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) and 𝕽<italic><sub>n</sub></italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) of analytic univalent functions defined by Erdelyi-Kober integral operator. We obtain coefficient inequalities, inclusion relationships involving the (<italic>n, δ</italic>)- neighborhoods, partial sums and integral mean inequalities for the functions that belongs to these classes. Also, subordinating factor sequence for the functions in the classes 𝔖<italic><sub>n</sub></italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) and 𝕽<italic><sub>n</sub></italic>(<italic>µ</italic>, <italic>a</italic>, <italic>b</italic>, <italic>ℓ</italic>, <italic>τ</italic>, <italic>γ</italic>) are derived.</p> </abstract>ARTICLEtrue Results of a Nonparametric Conditional Quantile Estimator in the Single Functional Index Modeling under Random Censorship<abstract> <title style='display:none'>Abstract</title> <p>The main objective of this paper is to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as an independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (<italic>cond-cdf</italic>) is introduced. Afterwards, we give an estimation of the quantiles by inverting this estimated <italic>cond-cdf</italic>, the asymptotic properties are stated when the observations are linked with a single-index structure. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.</p> </abstract>ARTICLEtrue intuitionistic fuzzy fractals by densifiability techniques<abstract> <title style='display:none'>Abstract</title> <p>We present a sequence of sets converging, under suitable conditions and respect to the Hausdorff intuitionistic fuzzy metric, to the attractor set of certain intuitionistic fuzzy iterated function systems. For this goal, we will introduce a <italic>fuzzy version</italic> of the so called <italic>α</italic>-dense curves which have been used by the author to approximate, with arbitrarily small and controlled error, the attractor set of certain (metric) iterated function systems. In this way, we relate the above mentioned concepts of the intuitionistic fuzzy metric spaces with the <italic>α</italic>-density theory.</p> </abstract>ARTICLEtrue A Certain Subclass Of Analytic Functions Defined By Linear Operator<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we introduce and study a new class <italic>k</italic> − <italic>ŨS</italic><italic><sub>s</sub></italic>(<italic>a, c, µ, γ, t</italic>) of analytic functions in the open unit disc <italic>U</italic> with negative coefficients and obtain coefficient estimates, neighborhoods and partial sums for functions <italic>f</italic> belonging to this class.</p> </abstract>ARTICLEtrue Inequalities Related to Wirtinger’s Result<abstract> <title style='display:none'>Abstract</title> <p>In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fejér’s inequality for convex functions and of Grüss’ type inequalities are also provided.</p> </abstract>ARTICLEtrue Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator<abstract> <title style='display:none'>Abstract</title> <p>In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass <italic>T<sup>a,c</sup></italic><italic><sub>µ</sub></italic>(<italic>α, β, γ, A, B</italic>) of starlike functions with negative coefficient. Various properties like coefficient estimates, neighbourhood results, integral means, partial sums and subordination results are examined for this class.</p> </abstract>ARTICLEtrue–derivative on univalent functions associated with subordination structure<abstract> <title style='display:none'>Abstract</title> <p>By means of Jackson’s (<italic>p, q</italic>)–derivative a new class of univalent functions based on subordination is defined. We evoke some geometric properties such as coefficient estimate, convolution preserving, convexity and radii properties of this class of functions are obtained.</p> </abstract>ARTICLEtrue Radius for Goodman-Ronning Type Harmonic Univalent Functions<abstract> <title style='display:none'>Abstract</title> <p>In this paper we obtain the sharp Bohr radius, Bohr-Rogosinski radius, improved Bohr-radius and refined Bohr radius for the functions in the class <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2021-0018_eq_001.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mover accent="true"><mml:mi>H</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>γ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> <tex-math>G_{\bar H}^0\left( \gamma \right)</tex-math> </alternatives> </inline-formula> of Goodman-Ronning type harmonic univalent functions with negative coeffcients.</p> </abstract>ARTICLEtrue Fekete-Szego Theorem for Close-to-convex Functions Associated with The Koebe Type Function<abstract> <title style='display:none'>Abstract</title> <p>This paper deals with the class <italic>S</italic> containing functions which are analytic and univalent in the open unit disc <italic>U</italic> = {<italic>z</italic> ∈ ℂ : |<italic>z</italic>| &lt; 1}. Functions <italic>f</italic> in <italic>S</italic> are normalized by <italic>f</italic>(0) = 0 and <italic>f</italic>′(0) = 1 and has the Taylor series expansion of the form <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2021-0019_eq_001.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>z</mml:mi><mml:mo>+</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mo>∞</mml:mo></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msub><mml:msup><mml:mrow><mml:mi>z</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:mrow></mml:math> <tex-math>f\left( z \right) = z + \sum\limits_{n = 2}^\infty {{a_n}{z^n}}</tex-math> </alternatives> </inline-formula>. In this paper we investigate on the subclass of <italic>S</italic> of close-to-convex functions denoted as <italic>C</italic><italic><sub>gα</sub></italic>(<italic>λ, δ</italic>) where function <italic>f</italic> ∈ <italic>C</italic><italic><sub>gα</sub></italic>(<italic>λ, δ</italic>) satisfies <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2021-0019_eq_002.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:mo>Re</mml:mo><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>λ</mml:mi></mml:mrow></mml:msup><mml:mfrac><mml:mrow><mml:mi>z</mml:mi><mml:msup><mml:mi>f</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mi>g</mml:mi><mml:mi>α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow> <mml:mo>}</mml:mo></mml:mrow></mml:mrow></mml:math> <tex-math>{\mathop{\rm Re}\nolimits} \left\{ {{e^{i\lambda }}{{zf'\left( z \right)} \over {g\alpha \left( z \right)}}} \right\}</tex-math> </alternatives> </inline-formula> for <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2021-0019_eq_003.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>|</mml:mo></mml:mrow><mml:mo>&lt;</mml:mo><mml:mfrac><mml:mi>π</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:math> <tex-math>\left| \lambda \right| &lt; {\pi \over 2}</tex-math> </alternatives> </inline-formula>, cos(<italic>λ</italic>) <italic>&gt; δ</italic>, 0 ≤ <italic>δ &lt;</italic> 1, 0 ≤ <italic>α</italic> ≤ 1 and <inline-formula> <alternatives> <inline-graphic xmlns:xlink="" xlink:href="graphic/j_gm-2021-0019_eq_004.png"/> <mml:math xmlns:mml="" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>g</mml:mi></mml:mrow><mml:mi>α</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mi>z</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>α</mml:mi><mml:mi>z</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math> <tex-math>{g_\alpha } = {z \over {{{\left( {1 - \alpha z} \right)}^2}}}</tex-math> </alternatives> </inline-formula>. The aim of the present paper is to find the upper bound of the Fekete-Szego functional |<italic>a</italic><sub>3</sub> − <italic>µa</italic><sub>2</sub><sup>2</sup>| for the class <italic>C</italic><sub>g</sub><italic><sub>α</sub></italic>(<italic>λ, δ</italic>). The results obtained in this paper is significant in the sense that it can be used in future research in this field, particularly in solving coefficient inequalities such as the Hankel determinant problems and also the Fekete-Szego problems for other subclasses of univalent functions.</p> </abstract>ARTICLEtrue Subclasses of Bi-Univalent Functions based on the Fibonacci Numbers<abstract> <title style='display:none'>Abstract</title> <p>In this work, by using the Al-Oboudi differential operator and the rule of subordination, we introduced the new subclasses <italic>D</italic><italic><sup>n,ρ</sup></italic><sub>Σ,</sub><italic><sub>δ</sub></italic>(Φ) and <italic>F</italic><italic><sup>n,α</sup></italic><sub>Σ,</sub><italic><sub>δ</sub></italic>(Φ) of the bi-univalent functions. Likewise, we use the Fibonacci numbers to derive the initial coefficients bounds for |<italic>a</italic><sub>2</sub>| and |<italic>a</italic><sub>3</sub>| of the bi-univalent function subclasses.</p> </abstract>ARTICLEtrue surfaces obtained by curves in the lightlike cone<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we consider the ruled surfaces obtained the lightlike curve in the 2-dimensional lightlike cone according to the frame given in [7]. We obtain necessary and sufficient conditions for the ruled surfaces to be minimal and to have a harmonic Gauss map. Then we see that the ruled surface is minimal if and only if it has a harmonic Gauss map.</p> </abstract>ARTICLEtrue distribution: properties and applications<abstract> <title style='display:none'>Abstract</title> <p>A new continuous distribution is proposed using Epanechnikov kernel function and the exponential distribution. This distribution is called the Epanechnikov-exponential distribution. Some properties of this distribution are studied. A simulation study is conducted to calculate the mean and the standard deviation of this distribution and to investigate the behavior of MLE to conserve the consistency property. An application to a real data set is conducted, it showed that he new distribution is more flexible than the exponential distribution.</p> </abstract>ARTICLEtrue solutions for a (3+1)-dimensional nonlinear evolution equation<abstract> <title style='display:none'>Abstract</title> <p>Via Hirota bilinear method and perturbation technique, a more general <italic>N-</italic>soliton solution with a parameter <italic>p</italic> for a (3+1)-dimensional nonlinear evolution equation is obtained. And two <italic>N</italic>-soliton solutions in terms of Wronskian determinant are also presented in the case of <italic>p</italic> = 1 and <italic>p</italic> = 3.</p> </abstract>ARTICLEtrue modified Bernstein-Stancu operators<abstract> <title style='display:none'>Abstract</title> <p>This paper is dealing with a class of operators fixing exponential functions. We study its convergence and an asymptotic formula is obtained. Finally, a comparison is stated, that shows that in a certain particular cases the new sequence approximates better than the classical ones.</p> </abstract>ARTICLEtrue estimates for a subclass of bi-univalent functions involving the -derivatives operator<abstract> <title style='display:none'>Abstract</title> <p>In this current study, we introduce and investigate a new subclass of holormorphic and bi-univalent functions 𝕰 <italic><sup>η,ϕ</sup></italic><italic><sub>q</sub></italic>(<italic>ϑ</italic>) in the unit disk λ associated with <italic>q</italic>-derivative operator. The coefficient estimates |<italic>b</italic><sub>2</sub>| and |<italic>b</italic><sub>3</sub>| on the new subclass are obtained and important results are indicated.</p> </abstract>ARTICLEtrue general common fixed point theorem for a pair of mappings in - metric spaces<abstract> <title style='display:none'>Abstract</title> <p>The purpose of this paper is to prove a common fixed point theorem for a pair of mappings satisfying an implicit relation, generalizing the main results from [6], [10], [11], [13] and other papers.</p> </abstract>ARTICLEtrue unique common fixed point for a family of set-valued mappings<abstract> <title style='display:none'>Abstract</title> <p>The main purpose of this paper is to establish some common fixed point theorems for single and set-valued mappings, under strict contractive conditions with no continuity, no completeness, no inclusions and without using neither compactness nor closeness. These theorems improve the results of Fisher [8], Ahmed [1] and [2], and others. Also, common fixed point theorems for two hybrid pairs satisfying a contractive condition of integral type are given improving the results of [3], [4] and [6].</p> </abstract>ARTICLEtrue methods for extended general variational inequalities<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we suggest and analyze a new approximation schemes (3) to solve the extended general variational inequalities (2), which were introduced by Muhammad Aslam Noor (see[7, 9]). Using the projection operator technique, we establish the equivalence between the extended general variational inequalities and the fixed-point problem. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.</p> </abstract>ARTICLEtrue of classical and modified operators<abstract> <title style='display:none'>Abstract</title> <p>We are concerned with a family of Markov operators and some modifications of them. Differences involving such operators are studied. We compare their Voronovskaya formulas and determine the limits of their iterates.</p> </abstract>ARTICLEtrue polynomials and their applications to a certain family of bi-univalent functions defined by Wanas operator<abstract> <title style='display:none'>Abstract</title> <p>In this article, by making use of Horadam polynomials, we introduce and investigate a certain family 𝔗<sub>Σ</sub> (λ, α, β, <italic>k</italic>, <italic>γ</italic>; <italic>x</italic>) of analytic and biunivalent functions associated with Wanas operator which defined in the open unit disk 𝕌. We establish upper bounds for the initial Taylor-Maclaurin coefficients and obtain the Fekete-Szegö inequality of functions belonging to this family. We also point out several certain special cases for our results.</p> </abstract>ARTICLEtrue