ON ABEL CONVERGENT SERIES OF FUNCTIONS
Keywords:pointwise convergence, uniform convergence, Abel convergence.
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 < ":
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