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3 Fasciculi Mathematici

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Common fixed points of a three-step iteration with errors of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense in Banach spaces

Okeke G A, Olaleru J. O.

Fasciculi Mathematici

2014

Nr 52

93--115

In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Our results extends, improves, unifies and generalizes the results of [13], [25] and [27].

The equivalence of Jungck-type iterations for generalized contractive-like operators in a Banach space

Olaleru J. O., Hudson A.

Fasciculi Mathematici

2011

Nr 47

47--61

We show that the convergences of Jungck, Jungck- Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep itera¬tion processes are equivalent for a class of generalized contractive- like operators defined on a Banach space. Our results are general¬izations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones in literature.

The convergence of Jungck-type iterative schemes for generalized contractive-like operators

Olaleru J. O., Akewe H.

Fasciculi Mathematici

2010

Nr 45

87-98

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like opera- tors defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa and Jungck-Noor itera- tions can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations and extensions of the work of Olatinwo and Imoru [13], Olatinwo [14-15]. Consequently, several results in literature are generalized.