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Some stability results for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space using two new iterative processes of Kirk-type

Olatinwo M. O.

Fasciculi Mathematici

2010

Nr 43

101-114

In this paper, we examine the stability of Kirk-Ishikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some of the results of Harder and Hicks [11], Rhoades [26, 27], Osilike [23], Berinde [2, 3] as well as Imoru and Olatinwo [12].