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

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.319-357
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• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.667-678
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• 2015

The aim of this paper is to prove strong convergence theorem by a modified three step iterative process with errors for three nonexpansive mappings in the frame work of uniformly smooth Banach spaces. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern type and weak convergence like Ishikawa type iteration schemes. Our result extend and generalize the result of S. H. Khan, Kim and Xu and many other authors.

• East Asian mathematical journal
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• v.36 no.5
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• pp.571-581
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• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.75-82
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• 2003

In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al. (2001) and generalize the recent result of Kim(2000).

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.293-299
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• 2008

In this paper, we prove strong convergence theorems for a finite family of uniformly L-Lipschitzian mappings by a cyclic iterative algorithm in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.409-425
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• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.375-385
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• 2014

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1499-1506
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• 2010

IIn this paper, we suggest and analyze a modified Mann's algorithm based on the CQ method for pseudo-contractive mappings in Hilbert spaces. Further, we prove a strong convergence theorem according to the proposed algorithm for pseudo-contractive mappings.

• East Asian mathematical journal
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• v.25 no.1
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• pp.97-105
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• 2009

In this paper, we prove a strong convergence theorem for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the modified Ishikawa iteration method. Our results improved and extend the corresponding results announced by many others.