Browsing by Author "Aslan, Resat"

Now showing 1 - 5 of 5

Approximation by a New Stancu Variant of Generalized (Λ, Μ)-Bernstein Operators
(Elsevier, 2024) Cai, Qing-Bo; Aslan, Resat; Ozger, Faruk; Srivastava, Hari Mohan
The primary objective of this work is to explore various approximation properties of Stancu variant generalized (lambda, mu)-Bernstein operators. Various moment estimates are analyzed, and several aspects of local direct approximation theorems are investigated. Additionally, further approximation features of newly defined operators are delved into, such as the Voronovskaya-type asymptotic theorem and pointwise estimates. By comparing the proposed operator graphically and numerically with some linear positive operators known in the literature, it is evident that much better approximation results are achieved in terms of convergence behavior, calculation efficiency, and consistency. Finally, the newly defined operators are used to obtain a numerical solution for a special case of the fractional Volterra integral equation of the second kind.
A Note on a General Sequence of Λ -Szasz Kantorovich Type Operators
(Springer Heidelberg, 2024) Rao, Nadeem; Ayman-Mursaleen, Mohammad; Aslan, Resat
In the present manuscript, we study the approximation properties of modified Sz & aacute;sz Kantorovich operators with a new modification of blending type which depends on parameters, lambda is an element of [-1, 1] and rho > 0. Further, we prove a Korovkin-type approximation theorem and obtain the rate of convergence of these operators. Next, their graphical depiction, error analysis and convergence behaviour of these operators for the different functional spaces are discussed. Moreover, univariate and bivariate version of these sequences of operators are introduced in their respective blocks. Rate of convergence, order of approximation, local approximation, global approximation in terms of weight function and A-statistical approximation results are investigated via first and second-order modulus of smoothness, Lipschitz classes, Peetre's K-functional in different spaces of functions.
On a New Type of Szasz-Chlodowsky Operators in Terms of 2D Appell Polynomials
(Univ Nis, Fac Sci Math, 2024) Karakilic, Ilhan; Aslan, Resat; Ali, Mahvish; Turhan, Nezihe
The main goal of this research is to obtain several approximation properties of Kantorovich variant Szasz-Chlodowsky operators based on 2D Appell Polynomials. We provide a connection between weighted B-statistical convergence (WBSC) and the rate of WBSC concepts and approximation theory. We also prove a Voronovskaja theorem related to WBSC. Finally, we consider certain examples and discuss the advantages of proposed operators via certain numerical results.
Rate of Approximation of Blending Type Modified Univariate and Bivariate Λ-Schurer Operators
(Elsevier, 2024) Aslan, Resat
In this work, we investigate some approximation properties of blending type univariate and bivariate SchurerKantorovich operators based on shape parameter lambda is an element of [-1, 1]. We evaluate some moment estimates and obtain several direct theorems. Next, we construct the bivariate version of proposed operators and compute rate of approximation with the partial and complete modulus of continuity. Moreover, we present certain graphical and numerical results for univariate and bivariate versions of these operators.
Some Approximation Properties of Riemann-Liouville Type Fractional Bernstein-Stancu Operators With Order of Α
(Springer int Publ Ag, 2025) Aslan, Resat
The main intent of this paper is to examine some approximation properties of Riemann-Liouville type fractional Bernstein-Stancu-Kantorovich operators with order of alpha. We derive some moment estimates and show the uniform convergence theorem, degree of convergence with respect to the usual modulus of continuity, class of Lipschitz-type continuous functions and as well as Peetre's K-functional. Furthermore, we present various graphical and numerical examples to demonstrate and compare the effectiveness of the proposed operators. Also, we construct bivariate extension of the related operators and consider order of approximation by means of partial and complete modulus of continuity. Further, we provide a graphical representation and an error of approximation table to show the behavior order of convergence of bivariate form of discussed operators.