On the degree of approximation of Fourier series based on a certain class of product deferred summability means

Abstract

Abstract In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions. We then estimate the degree of approximation of Fourier series of an arbitrary periodic function in the generalized Zygmund class based upon our proposed product deferred summability means. Moreover, we discuss some important concluding remarks in connection with our findings. Finally, we suggest a direction for future studies on this subject, which are based upon the basic notion of statistical product deferred summability means of Fourier series of arbitrary periodic functions in the generalized Zygmund class.

Keywords

• Degree of approximation
• Zygmund modulus of continuity
• Fourier series of arbitrary periodic functions
• Deferred Euler summability mean
• Deferred Nörlund summability mean
• Product deferred summability mean