On Best Multiplier Approximation of k-Monotone by Trigonometric Polynomial

Abstract

The main goal of this paper is to study the degree of the best multiplier approximation of monotone unbounded functions in L_(p,λ_n)-space on the closed interval [-π,π] by means of K-functional, which we represented with, K(f,L_(p,λ_n ),W_(p,λ_n)^1,W ̃_(p,λ_n)^1), defined by the W_(p,λ_n)^1 and W ̃_(p,λ_n)^1 that are referred to during this research. In addition, we have established a set of definitions, concepts and some useful lemmas that are needed in our work.

Keywords

• Multiplier integral
• Multiplier averaged modulus of smoothness
• Multiplier norm.