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Convergence theorems by hybrid projection methods for Lipschitz-continuous monotone mappings and a countable family of nonexpansive mappings

100%
Plubtieng S., Kumam P.
Banach Center Publications
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2011
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tom 92
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nr 1
283-297
EN
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 family of nonexpansive mappings. Moreover, we apply our result to the problem for finding a common fixed point of two mappings, such that one of these mappings is nonexpansive and the other is taken from the more general class of Lipschitz pseudocontractive mappings. Our results extend and improve the results of Nadezhkina and Takahashi [SIAM J. Optim. 16 (2006), 1230-1241], Zeng and Yao [Taiwanese J. Math. 10 (2006), 1293-1303] and many authors.
2
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An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

100%
Katchang P., Kumam P.
Banach Center Publications
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2011
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tom 92
|
nr 1
177-196
EN
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four sets. Our results improve and extend the corresponding results of Peng and Yao [Math. Comput. Modelling 49 (2009), 1816-1828], Plubtieng and Sriprad [Fixed Point Theory Appl. 2009, Article ID 567147] and some well-known results in the literature.
3
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Strong convergence theorems of a new hybrid projection method for finite family of two hemi-relatively nonexpansive mappings in a Banach space

100%
Wattanawitoon K., Kumam P.
Banach Center Publications
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2011
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tom 92
|
nr 1
379-390
EN
In this paper, we prove strong convergence theorems of the hybrid projection algorithms for finite family of two hemi-relatively nonexpansive mappings in a Banach space. Using this result, we also discuss the resolvents of two maximal monotone operators in a Banach space. Our results modify and improve the recently ones announced by Plubtieng and Ungchittrakool [Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007), 103-115], Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005), 257-266] and many others.
4
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Fixed Point Results Satisfying Rational Type Contractive Conditions in Complex Valued Metric Spaces

81%
Kumam P., Sarwar M., Zada M. B.
Annales Mathematicae Silesianae
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2016
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tom 30
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nr 1
89-110
EN
The aim of this manuscript is to establish fixed point results satisfying contractive conditions of rational type in the setting of complex valued metric spaces. The derived results generalize and extend some well known results in the existing literature.
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