Bivariate Cheney-Sharma operators on simplex
G\"ulen Ba\c{s}canbaz-Tunca, Ay\c{s}eg\"ul Eren\c{c}in, Hatice G\"ul, \.Ince \.Ilarslan
TL;DR
This paper introduces bivariate Cheney-Sharma operators that are not tensor products, demonstrating their ability to preserve Lipschitz continuity and modulus of continuity properties of functions.
Contribution
It presents a novel class of bivariate Cheney-Sharma operators and analyzes their property-preserving capabilities, expanding approximation theory.
Findings
Operators preserve Lipschitz condition of functions
Operators maintain properties of the modulus of continuity
Non-tensor product construction of bivariate operators
Abstract
In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction. Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function f and also the properties of the modulus of continuity function when f is a modulus of continuity function.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Holomorphic and Operator Theory · Advanced Banach Space Theory