Approximation by Riemann–Liouville type fractional α$$ \alpha $$‐Bernstein–Kantorovich operators

Author:

Berwal Sahil1,Mohiuddine S. A.23,Kajla Arun1ORCID,Alotaibi Abdullah3

Affiliation:

1. School of Basic Sciences Central University of Haryana Haryana India

2. Department of General Required Courses, Mathematics, The Applied College King Abdulaziz University Jeddah Saudi Arabia

3. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science King Abdulaziz University Jeddah Saudi Arabia

Abstract

In this research paper, we construct a new sequence of Riemann–Liouville type fractional ‐Bernstein–Kantorovich operators. We prove a Korovkin type approximation theorem and discuss the rate of convergence with the first order modulus of continuity of these operators. Further, we study Voronovskaja type theorem, quantitative Voronovskaya type theorem, Chebyshev–Grüss inequality and Grüss–Voronovskaya type theorem.

Publisher

Wiley

Reference43 articles.

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2. Approximation of functions by a new family of generalized Bernstein operators

3. Construction of a new family of Bernstein-Kantorovich operators

4. Sur certains développements suivant les polynômes de la forme de S. Bernstein, I, II;Kantorovich L. V.;CR Acad. URSS,1930

5. Asymptotic Formulas for Generalized Szász–Mirakyan Operators

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