Some fixed point iteration procedures.
Rhoades, B.E. (1991)
International Journal of Mathematics and Mathematical Sciences
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Rhoades, B.E. (1991)
International Journal of Mathematics and Mathematical Sciences
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Memudu Olaposi Olatinwo (2008)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, following the concepts in [5, 7], we shall establish a convergence result in a uniformly convex Banach space using the Jungck–Mann iteration process introduced by Singh et al [13] and a certain general contractive condition. The authors of [13] established various stability results for a pair of nonself-mappings for both Jungck and Jungck–Mann iteration processes. Our result is a generalization and extension of that of [7] and its corollaries. It is also an improvement...
Alfred Olufemi Bosede (2010)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, we establish some generalizations to approximate common fixed points for selfmappings in a normed linear space using the modified Ishikawa iteration process with errors in the sense of Liu [10] and Rafiq [14]. We use a more general contractive condition than those of Rafiq [14] to establish our results. Our results, therefore, not only improve a multitude of common fixed point results in literature but also generalize some of the results of Berinde [3], Rhoades [15] and...
Lemaire, B. (1996)
Serdica Mathematical Journal
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The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces.
Rafiq, Arif (2006)
Applied Mathematics E-Notes [electronic only]
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Roux, D., Singh, S.P. (1989)
International Journal of Mathematics and Mathematical Sciences
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Alfred Olufemi Bosede (2011)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.
Tatjana Petek (2004)
Studia Mathematica
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Let H be an infinite-dimensional complex Hilbert space. We give a characterization of surjective linear mappings on B(H) that preserve similarity in both directions.
Kazimierz Goebel, Ewa Sędłak (2009)
Annales UMCS, Mathematica
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Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.