Limit Summability of Functions Relative to Sequences of Polynomials of a Fixed Degree

Abstract

The topic of limit summability of functions was introduced by Hooshmand in 2001. Thereafter, some other types of summability of functions such as analytic summability of real and complex functions were introduced and studied by him. Motivated by the limit and analytic summabilities together with fractional sums, we introduce the concept of limit summability of functions relative to a sequence of polynomials of a fixed degree. In this regard, we try to extend the relevant
results of limit summability for this topic. Also, we show that this type of summability covers a wider range of functions.