On the approximation by Bezier-Paltanea operators based on Gould Hopper polynomials

In the present article, we give a Bezier variant of Paltanea operators whichinvolves Gould Hopper polynomials. First, we investigate rate of convergence by using Ditzian-Totik modulus of smoothness, weighted modulus of continuity and also for class ofLipschitz function. Furthermore, we obtain the quantitative Voronovskaja type theoremin terms of Ditzian-Totik modulus of smoothness. In the last section, we study the rate ofpoint-wise convergence for the functions having a derivative of bounded variation

A Generalization of Szász–Mirakyan Operators Based on α Non-Negative Parameter

The main purpose of this paper is to define a new family of Szász–Mirakyan operators that depends on a non-negative parameter, say α. This new family of Szász–Mirakyan operators is crucial in that it includes both the existing Szász–Mirakyan operator and allows the construction of new operators for different values of α. Then, the convergence properties of the new operators with the aid of the Popoviciu–Bohman–Korovkin theorem-type property are presented. The Voronovskaja-type theorem and rate of convergence are provided in a detailed proof. Furthermore, with the help of the classical modulus of continuity, we deduce an upper bound for the error of the new operator. In addition to these, in order to show that the convex or monotonic functions produced convex or monotonic operators, we obtain shape-preserving properties of the new family of Szász–Mirakyan operators. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Moreover, we compare this operator with its classical correspondence to show that the new one has superior properties. Finally, some numerical illustrative examples are presented to strengthen our theoretical results

Stability Results in Intuitionistic Fuzzy Normed Spaces for a Cubic Functional Equation

Abstract: In this paper, we determine some stability results concerning the cubic functional equation kf(x+ky)+f(kx−y) = k(k2 +1) [f(x+y)+f(x−y)]+(k 2 4 −1)f(y), where k ≥ 2 is a fixed integer, in the setting of intuitionistic fuzzy normed spaces (IFNS). Further we study the intuitionistic fuzzy continuity through the existence of a certain solution of a fuzzy stability problem for approximately cubic functional equation