Approximation of Kantorovich-type Generalization of (p,q) - Bernstein type Rational Functions Via Statistical Convergence

Main Article Content

Hayatem Hamal*

Abstract

In this paper, we use the modulus of continuity to study the rate of A-statistical convergence of the Kantorovich-type (p,q) - analogue of the Balázs–Szabados operators by using the statistical notion of convergence.


Mathematics subject classification: Primary 4H6D1; Secondary 4H6R1; 4H6R5.

Article Details

Hamal, H. (2024). Approximation of Kantorovich-type Generalization of (p,q) - Bernstein type Rational Functions Via Statistical Convergence. International Journal of Physics Research and Applications, 7(1), 019–025. https://doi.org/10.29328/journal.ijpra.1001080
Mini Reviews

Copyright (c) 2024 Hamal H.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Balázs K. Approximation by Bernstein type rational function. Acta Math Acad Sci Hungar. 1975; 26; 123-134.

Balázs K, Szabados J. Approximation by Bernstein type rational function II. Acta Math Acad Sci Hungar. 1982; 40: 331-337.

Doğru O. On Statistical Approximation Properties of Stancu type bivariate generalization of Balázs-Szabados operators. Proceedings. Int. Conf. on Numer. Anal. and Approx. Theory Cluj-Napoca, Romania. 2006; 179-194.

İspir N, ӧzkan EY. Approximation Properties of Complex Balázs-Szabados Operators in Compact Disks. J Inequal Appl. 2013; 361.

Mahmudov NI. Approximation Properties of the Balázs-Szabados Complex Operators in the case. Comput. Methods Funct Theory. 2016; 16: 567-583.

Özkan EY. Approximation Properties of Kantorovich type Balázs-Szabados operators. Demonstr Math. 2019; 52: 10-19.

Mahmudov NI, Sabancigil P. Approximation Theorems for Bernstein-Kantorovich Operators. 2013; 27(4): 721-730.

Hamal H, Sabancigil P. Some Approximation Properties of new Kantorovich type analogue of Balazs-Szabados Operators. Journal of Inequalities and Applications.2020; 159.

Mursaleen M, Ansari KJ, Khan A. On (p,q) - analogue of Bernstein operators. Appl Math Comput. 2015; 266; 874–882.

Mursaleen M, Sarsenbi AM, Khan T. On (p,q)-analogue of two parametric Stancu-Beta operators. J Inequal Appl 2016; 190: 1-15.

Mursaleen M, Khan F, Khan A. Statistical approximation for new positive linear operators of Lagrange type. Appl Math Comput. 2014; 232: 548–558.

Mursaleen M, Ansari KJ, Khan A. Approximation by (p,q)-Lorentz polynomials on a compact disk. Complex Anal Oper Theory. 2016; 10: 1725-1740.

Mursaleen M, Nasiruzzaman M, Khan A, Ansari KJ. Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers. Filomat. 2016; 30: 639–648.

Mursaleen M, Ansari KJ, Khan A. Some approximation results for Bernstein-Kantorovich operators based on (p,q)-calculus. UPB Sci Bull Ser A Appl Math Phys. 2016; 78:129–142.

Mursaleen M, Ansari KJ, Khan A. Some approximation results by (p,q)-analogue of Bernstein-Stancu operators. Appl Math Compt. 2015; 246: 392-402. Corrigendum: Appl Math Comput. 2015; 269: 744-746.

Acar T, Aral A, Mohiuddine SA. On Kantorovich modification of (p,q)-Baskakov operators. J Inequal Appl. 2016; 98. https://doi.org/10.1186/s13660-016-1045-9.

Acar T, Aral A, Mohiuddine SA. On Kantorovich modification of (p,q) - Bernstein operators. Iran J Sci Technol Trans. A Sci. 2018; 42: 1459–1464.

Özkan EY, İspir N. Approximation by (p,q)-Analogue of Balázs-Szabados Operators. Filomat. 2018; 32: 2257–2271.

Hamal H, Sabancigil P. Some Approximation properties of new (p,q) - analogue of Balazs-Szabados Operators. Journal of Inequalities and Applications. 2021; 162.

Hamal H, Sabancigil P. Kantorovich Type Generalization of Bernstein Type Rational Functions Based on (p,q) – Integers. symmetry. 2022; 14.

Fast H. On statistical convergence /Sur la convergence statistigue, Colloquium Mathematicum. 1951; 2: 241-244.

Fridy JA. On statistical convergence. Journal analysis. 1985; 5: 301-313.

Gadjiev AD, Orhan C. Some approximation theorems via statistical convergence approximation. Rocky Mountain Journal of Mathematics. 2002; 32: 129-138.