• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.135-141
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• 2013

In this paper, we first talk about a more wide class of nonlinear mappings, Then, we deal with weak convergence theorems for generalized hybrid mappings in a Hilbert space.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.335-351
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• 2013

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

• East Asian mathematical journal
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• v.31 no.1
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• pp.77-89
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• 2015

We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under generalized non-linear contraction. An example supporting to our result has also been cited. We improve, extend and generalize several known results.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.1-17
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• 2022

We establish a common n-tupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction. An example is given to validate our results. We improve, extend and generalize several known results.

• East Asian mathematical journal
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• v.28 no.3
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• pp.305-320
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• 2012

The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.765-777
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• 2016

In this paper, we propose a new modied Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in a Hilbert space. Our results generalize and improve some existing results in the literature. A numerical example is given to illustrate the usability of our results.

• East Asian mathematical journal
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• v.28 no.3
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• pp.265-280
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• 2012

In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.583-607
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• 2010

The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang, and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no. 11, 5616?5628] and some other papers.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.199-214
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• 2015

We establish a common coupled fixed point theorem for hybrid pair of mappings under generalized Mizoguchi-Takahashi contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled oincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results. We improve, extend and generalize several known results.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.539-551
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• 2009

In this paper, we propose a modified hybrid algorithm and prove strong convergence theorems for a family of quasi-$\phi$-asymptotically nonexpansive mappings. Our results extend and improve the results by Nakajo, Takahashi, Kim, Xu, Su and some others.