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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Su, Yongfu, Shang, Meijuan, Wang, Dongxing (2008)
Banach Journal of Mathematical Analysis [electronic only]
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R.A. Rashwan, A.M. Saddeek (1994)
Collectanea Mathematica
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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...
Kittipong Sitthikul, Satit Saejung (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper, weak and strong convergence of finite step iteration sequences to a common fixed point for a pair of a finite family of nonexpansive mappings and a finite family of asymptotically nonexpansive mappings in a nonempty closed convex subset of uniformly convex Banach spaces are presented.
Zeqing Liu, Ravi P. Agarwal, Chi Feng, Shin Min Kang (2005)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The purpose of this paper is to establish some weak and strong convergence theorems of modified three-step iteration methods with errors with respect to a pair of nonexpansive and asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper generalize, improve and unify a few results due to Chang [1], Liu and Kang [5], Osilike and Aniagbosor [7], Rhoades [8] and Schu [9], [10] and others. An example is included to demonstrate that our results...
Somyot Plubtieng, Poom Kumam (2011)
Banach Center Publications
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In this paper, we introduce two iterative schemes for finding a common element of the set of a common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a Hilbert space by using the hybrid projection methods in the mathematical programming. Then we prove strong convergence theorems by the hybrid projection methods for a monotone, Lipschitz-continuous mapping and a countable...
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.