An operator version of the Korovkin theorem has recently been obtained by D. Popa. With motivation this result, we have extended it using a more powerful convergence which also includes ordinary convergence. We presented an example to illustrate strength our theorem.

*Correspondence: [email protected] 1Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India 2Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract The aim of this paper is to intro...

In this paper, we construct a form of linear positive operators with Brenke type polynomials as a generalization of Szasz-Durrmeyer operators. We obtain convergence properties of our operators with the help of the universal Korovkin-type property and calculate the order of approximation by using classical modulus of continuity. Explicit examples of our operators involving some orthonogal and d-...

In this paper, a generalization of the q-Meyer-K?nig and Zeller operators by means (p,q)- calculus is introduced. Some approximation results for (p,q)-analogue Meyer-K?nig denoted Mn,p,q 0 < q p ? 1 are obtained. Also we investigate classical statistical versions Korovkin type based on proposed operator. Furthermore, some graphical examples convergence presented.

The main purpose of this paper is to define a new family Szász–Mirakyan operators that depends on non-negative parameter, say ?. This crucial in it includes both the existing operator and allows construction for different values Then, convergence properties with aid Popoviciu–Bohman–Korovkin theorem-type property are presented. Voronovskaja-type theorem rate provided detailed proof. Furthermore...

In this work we introduce and investigate the ideas of statistical Riemann integrability, summability, Lebesgue integrability summability via deferred weighted mean. We first establish some fundamental limit theorems connecting these beautiful potentially useful notions. Furthermore, based upon our proposed techniques, Korovkin-type approximation with algebraic test functions. Finally, present ...