Inequalities for Approximation of New Defined Fuzzy Post-Quantum Bernstein Polynomials via Interval-Valued Fuzzy Numbers

Abstract

In this study, we introduce new defined fuzzy post-quantum Bernstein polynomials and present examples illustrating their existence. We investigate their approximation properties via interval-valued fuzzy numbers. We obtain a fuzzy Korovkin-type approximation result, and we obtain inequalities estimating the rate of fuzzy convergence for these polynomials by means of the fuzzy modulus of continuity and Lipschitz-type fuzzy functions. Lastly, we present a Voronovskaja type asymptotic result for fuzzy post-quantum Bernstein polynomials. The methods in this paper are crucial and symmetric in terms of extending the approximation results of these polynomials from the real function space to the fuzzy function space and the applicability to the other operators.

Keywords

• fuzzy number
• fuzzy Korovkin-type theorem
• fuzzy modulus of continuity
• asymptotic expansions