Riemann-Liouville type fractional a new generalization of Bernstein-Kantorovich operators

TL;DR

This paper introduces a new fractional generalization of Bernstein-Kantorovich operators using Riemann-Liouville derivatives, analyzing their approximation properties and convergence through theoretical, numerical, and graphical methods.

Contribution

It presents a novel Riemann-Liouville fractional approach to Bernstein-Kantorovich operators, including their bivariate extension and approximation analysis.

Findings

Operators demonstrate effective convergence and accuracy.

Numerical and graphical results confirm theoretical approximation properties.

Bivariate operators extend the applicability to higher dimensions.

Abstract

Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to numerous scientific challenges not only in mathematics but also in fields like as physics and engineering etc. In the present work, we construct Riemann-Liouville type fractional a new generalization of Bernstein-Kantorovich type operators. First, we obtain the moment and central moments from some basic calculations. Also, we study several direct and local approximation outcomes of the constructed operators. Next, we serve up certain graphical and numerical results to demonstrate the convergence, accuracy and significance of constructed operators. Further, we provide bivariate version of the newly constructed operators and establish degree of approximation through of partial and complete modulus of continuity. Lastly, we present some graphical representations and maximum error of approximation tables to verify the convergence behavior of bivariate form of related operators based on various parameters.