ON ABEL CONVERGENT SERIES OF FUNCTIONS (JOURNAL OF ADVANCES IN MATHEMATICS, 2016)
In this paper, we are concerned with Abel uniform convergence and Abel pointwise convergence of series of real functions where a series of functions Î£ fn is called Abel uniformly convergent to a function f if for each " > 0 there is a _ > 0 such that jfx(t) ô€€€ f(t)j < " for 1 ô€€€ _ < x < 1 and 8t 2 X, and a series of functions Î£ 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 ô€€€ _ < x < 1 jfx(t) ô€€€ f(t)j < ":