ON ABEL CONVERGENT SERIES OF FUNCTIONS

Abstract

In this paper, we are concerned with Abel uniform convergence and Abel pointwise convergence of series of real functions where a series of functions Σ fn is called Abel uniformly convergent to a function f if for each " > 0 there is a _ > 0 such that jfx(t) 􀀀 f(t)j < " for 1 􀀀 _ < x < 1 and 8t 2 X, and a series of functions Σ fn is called Abel pointwisely convergent to f if for each t 2 X and 8" > 0 there is a _("; t) such that for 1 􀀀 _ < x < 1 jfx(t) 􀀀 f(t)j < ":