Approximation of Kantorovich-type Generalization of (p,q) - Bernstein type Rational Functions Via Statistical Convergence
Article Sidebar
Main Article Content
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
Copyright (c) 2024 Hamal H.
This work is licensed under a Creative Commons Attribution 4.0 International License.
The International Journal of Physics Research and Applications is committed in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. In order to use the Open Access paradigm to the maximum extent in true terms as free of charge online access along with usage right, we grant usage rights through the use of specific Creative Commons license.
License: Copyright © 2017 - 2025 | 
Open Access by International Journal of Physics Research and Applications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at Heighten Science Publications Inc.
With this license, the authors are allowed that after publishing with the journal, they can share their research by posting a free draft copy of their article to any repository or website.
Compliance 'CC BY' license helps in:
| Permission to read and download | ✓ |
| Permission to display in a repository | ✓ |
| Permission to translate | ✓ |
| Commercial uses of manuscript | ✓ |
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific 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.