Numerical analysis of fractional Volterra integral equations via Bernstein approximation method

F Usta - Journal of Computational and Applied Mathematics, 2021 - Elsevier
In this study, Bernstein approximation method has been applied along with Riemann–
Liouville fractional integral operator to solve both the second and the first kind of fractional …

Bernstein operator method for approximate solution of singularly perturbed Volterra integral equations

F Usta, M Akyiğit, F Say, KJ Ansari - Journal of Mathematical Analysis and …, 2022 - Elsevier
An approximate solution of integral equations takes an active role in the numerical analysis.
This paper presents and tests an algorithm for the approximate solution of singularly …

Approximation of functions by a new construction of Bernstein‐Chlodowsky operators: theory and applications

F Usta - Numerical Methods for Partial Differential Equations, 2021 - Wiley Online Library
The main motivation of this paper is to provide a generalization of Bernstein‐Chlodowsky
type operators which depend on function τ by means of two sequences of functions. The …

Approximation by modified q-Gamma type operators via A-statistical convergence and power series method

JK Singh, PN Agrawal, A Kajla - Linear and Multilinear Algebra, 2022 - Taylor & Francis
In this article, we introduce aq-analogue of the operators defined by Usta and Betus (Linear
Multilinear Algebra, DOI: 10.1080/03081087.2020. 1791033 (2020)) and find a general …

Approximation properties of a new family of Gamma operators and their applications

R Özçelik, EE Kara, F Usta, KJ Ansari - Advances in Difference Equations, 2021 - Springer
The present paper introduces a new modification of Gamma operators that protects
polynomials in the sense of the Bohman–Korovkin theorem. In order to examine their …

A Generalization of Szász–Mirakyan Operators Based on α Non-Negative Parameter

KJ Ansari, F Usta - Symmetry, 2022 - mdpi.com
The main purpose of this paper is to define a new family of Szász–Mirakyan operators that
depends on a non-negative parameter, say α. This new family of Szász–Mirakyan operators …

Approximation of functions by a new type of Gamma operators

Ö Betus, F Usta - Numerical Methods for Partial Differential …, 2023 - Wiley Online Library
In this article, a new type of Gamma operators which preserves 1 and x 2 has been
presented and tested. In order to show the approximation properties of the newly defined …

Approximation by q‐Post‐Widder Operators Based on a New Parameter

Q Lin - Abstract and Applied Analysis, 2024 - Wiley Online Library
The purpose of this paper is to introduce q‐Post–Widder operators based on a new
parameter and study their approximation properties. The moments and central moments are …

Approximation by modified q‐Gamma type operators in a polynomial weighted space

JK Singh, PN Agrawal, A Kajla - Mathematical Methods in the …, 2023 - Wiley Online Library
In this research article, we construct aq q‐analogue of the operators defined by Betus and
Usta (2020) and study approximation properties of these operators in a polynomial weighted …

Approximation by modified -gamma-type operators

NL Braha - Journal of Inequalities and Applications, 2024 - Springer
The main object of this paper is to construct a new class of modified (p, q)-Gamma-type
operators. For this new class of operators, in section one, the general moments are find; in …