This paper is devoted to studying the statistical approximation properties of a sequence univariate and bivariate blending-type Bernstein operators that includes shape parameters ? ? positive integer. An estimate corresponding rates was obtained, Voronovskaja-type theorem given by weighted A-statistical convergence. A Korovkin-type provided for cases operators. Moreover, convergence behavior ne...

In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect a not necessarily additive set function. Based on their properties, quantitative estimate for nonlinear Korovkin approximation theorem associated Bernstein-Kantorovich-Choquet is proved. The paper also includes large generalization H\"{o}lder's inequality within framework mono...

In this work, we further develop the Korovkin-type approximation theory by utilizing a fuzzy logic approach and principles of neoclassical analysis, which is a new branch of fuzzy mathematics and extends possibilities provided by the classical analysis. In the conventional setting, the Korovkin-type approximation theory is developed for continuous functions. Here we extend it to the space of fu...

In the present work a Jain type modification of generalized Szász-Mirakyan operators that preserve constant and exponential mappings is presented. The introduction this operator helps to extend class functions. A particular expansion involving Lambert W-function established which used obtain properties operator. Moments, central moments, are presented with some limiting properties. Voronovskaya...

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion modulus smoothness, we also derive an associated concerning rate convergence these Furthermore, through example, illustrate that our summability- based Korovin has advantage over proved in seminal paper by Anastassiou (Stud. Univ. Babeş...

In this paper, we construct a new sequence of Riemann-Liouville type fractional Bernstein-Kantorovich operators $ K_{n}^{\alpha}(f;x) depending on parameter \alpha $. We prove Korovkin approximation theorem and discuss the rate convergence with first second order modulus continuity these operators. Moreover, introduce operator that preserves affine functions from Further, define bivariate case ...

* Correspondence: [email protected] Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Full list of author information is available at the end of the article Abstract In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of p...

We introduce the notion of weighted A-statistical convergence of a sequence, where A represents the nonnegative regular matrix. We also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence. Further, we give a rate of weighted A-statistical convergence and apply the classical Bernstein polynomial to construct an illustrative example in support of our...