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Fixed point theorems for a semigroup of total asymptotically nonexpansive mappings in uniformly convex Banach spaces

Suantai S., Phuengrattana W.

Opuscula Mathematica

2014

Vol. 34, no. 1

183--197

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.

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].

Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces

Bosede A. O.

Fasciculi Mathematici

2009

Nr 42

29-38

In this paper, we establish some fixed point theorems for Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces and deduce similar other results on Mann and Ishikawa iterations as special cases. Our results improve a multitude of recent results in the fixed point theory especially the result of Ciric [5].