Generalized Kantorovich modifications of positive linear operators

<p style='text-indent:20px;'>Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized convexity, invariant measures and iterates. Some known results from the literature are extended.</p>

GENERALIZED MULTIVARIATE PRABHAKAR TYPE FRACTIONAL INTEGRALS AND INEQUALITIES

We introduce here the mixed generalized multivariate Prabhakar type left and right fractional integrals and study their basic properties, such as preservation of continuity and their boundedness as positive linear operators. Then we produce an interesting variety of related multivariate left and right fractional Hardy type inequalities under convexity. We introduce also other related multivariate fractional integrals

Approximation by mixed positive linear operators based on second-kind beta transform

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

Statistical Approximation Properties of Some Positive Linear Operators

Statistical convergence is an important concept in functional analysis. In this work, we give a short survey about statistical convergence and statistical convergence of some positive linear operators to approximate functions.

Voronovskaja-Type Quantitative Results for Differences of Positive Linear Operators

We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating the theoretical aspects are presented.

VORONOVSKAYA TYPE RESULTS AND OPERATORS FIXING TWO FUNCTIONS

The present paper deals with positive linear operators which fix two functions. The transfer of a given sequence (Ln) of positive linear operators to a new sequence (Kn) is investigated. A general procedure to construct sequences of positive linear operators fixing two functions which form an Extended Complete Chebyshev system is described. The Voronovskaya type formula corresponding to the new sequence which is strongly influenced by the nature of the fixed functions is obtained. In the last section our results are compared with other results existing in literature.

Sharp inequalities for the rates of convergence of the iterates of some operators which preserve the constants

"In this paper we give estimates for the rates of convergence for the iterates of some positive linear operators which preserve only the constants. We obtain sharp inequalities when we use both continuous functions and di eren- tiable functions. We present some optimal results for the Cesaro, Stancu and Schurer operators."

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.