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ABSTRACT: We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties.
Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive
mappings in a uniformly convex and uniformly smooth Banach space.
Journal of Fixed Point Theory and Applications 04/2012; 5(2):201-225. · 0.78 Impact Factor
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ABSTRACT: The aim of this paper is to establish strong convergence theorems for a
strongly relatively nonexpansive sequence in a smooth and uniformly convex
Banach space. Then we employ our results to approximate solutions of the zero
point problem for a maximal monotone operator and the fixed point problem for a
relatively nonexpansive mapping.
02/2012;
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ABSTRACT: Some fundamental properties of resolvents of monotone operators in Banach spaces are investigated. Using them, we study the asymptotic behavior of the sequences generated by two modifications of the proximal point algorithm for monotone operators satisfying a range condition defined in Banach spaces.
TAIWANESE JOURNAL OF MATHEMATICS 03/2011; 15:259-281. · 0.56 Impact Factor
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ABSTRACT: In this paper, we introduce an iterative sequence for finding a solution of a maximal monotone operator in a uniformly convex Banach space. Then we first prove a strong convergence theorem, using the notion of generalized projection. Assuming that the duality mapping is weakly sequentially continuous, we next prove a weak convergence theorem, which extends the previous results of Rockafellar [SIAM J. Control Optim.
14 (1976), 877–898] and Kamimura and Takahashi [J. Approx. Theory
106 (2000), 226–240]. Finally, we apply our convergence theorem to the convex minimization problem and the variational inequality problem.
Set-Valued Analysis 11/2004; 12(4):417-429. · 0.55 Impact Factor
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ABSTRACT: The purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings. The method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping.
Nonlinear Analysis: Theory, Methods & Applications. 71(12).
