• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.105-118
• /
• 2010

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.51-65
• /
• 2011

In this paper, a composite iterative process is introduced for a generalized equilibrium problem and a pair of nonexpansive mappings. It is proved that the sequence generated in the purposed composite iterative process converges strongly to a common element of the solution set of a generalized equilibrium problem and of the common xed point of a pair of nonexpansive mappings.

• East Asian mathematical journal
• /
• v.26 no.3
• /
• pp.337-350
• /
• 2010

Strong convergence theorem of the explicit viscosity iterative scheme involving the sunny nonexpansive retraction for nonexpansive nonself-mappings is established in a reflexive and strictly convex Banach spaces having a weakly sequentially continuous duality mapping. The main result improves the corresponding result of [19] to the more general class of mappings together with certain different control conditions.

• East Asian mathematical journal
• /
• v.26 no.5
• /
• pp.627-639
• /
• 2010

In this paper, we introduce a new iterative sequence finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly-monotone mapping, the fixed point problem and the classical variational inequality problem. Our results improve and extend the corresponding results announced by many others.

• Journal of the Korean Mathematical Society
• /
• v.38 no.6
• /
• pp.1245-1260
• /
• 2001

A demi-closed theorem and some new weak convergence theorems of iterative sequences for asymptotically nonexpansive and nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results of [1],[8]-[10],[12],[13],[15],[16], and [18].

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.75-86
• /
• 2010

An iterative algorithm was been studied which can be viewed as an extension of the previously known algorithms for asymptotically nonexpansive mappings. Subsequently, we study the convergence problem of the proposed iterative algorithm for asymptotically nonexpansive mappings under some mild conditions in Banach spaces.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.125-137
• /
• 2008

In this paper, we first introduce some iterative sequences of Halpern type for asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces and then we discuss strong convergence for the iterative processes. The results presented in this paper extend, supplement and improve the correspoding main results of Reich [11], Shimizu and Takahashi [13], Shioji and Takahashi [15], [16] and Wittmann [18].

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.915-929
• /
• 2020

We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.665-678
• /
• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.5
• /
• pp.991-1002
• /
• 2011

An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.