• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.195-206
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• 2014

In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.

• 대한수학회지
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• 제43권1호
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• pp.1-9
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• 2006

Based on the Schauder fixed point theorem, we give a Leray-Schauder type fixed point theorem for countably condensing mappings in a more general setting and apply it to obtain eigenvalue results on condensing mappings in a simple proof. Moreover, we present a generalization of Sadovskii's fixed point theorem for count ably condensing self-mappings due to S. J. Daher.

• East Asian mathematical journal
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• 제26권5호
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• pp.599-605
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• 2010

In this paper, we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of an asymptotically strictly pseudocontractive mapping in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the two sets.

• 대한수학회논문집
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• 제25권3호
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• pp.419-426
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• 2010

In this paper, a three-step iterative method is considered for finding a common element in the set of fixed points of a non-expansive mapping and in the set of solutions of a variational inclusion problem in a real Hilbert space.

• 대한수학회보
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• 제51권2호
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• pp.479-499
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• 2014

In this paper, we propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.

• 대한수학회보
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• 제51권3호
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• pp.773-788
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• 2014

We introduce an iterative process which converges strongly to a common minimum-norm point of solutions of variational inequality problem for a monotone mapping and fixed points of a finite family of relatively nonexpansive mappings in Banach spaces. Our theorems improve most of the results that have been proved for this important class of nonlinear operators.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1445-1460
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• 2010

In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.457-478
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• 2015

In this paper we propose an iteration hybrid method for approximating a point in the intersection of the solution-sets of pseudomonotone equilibrium and variational inequality problems and the fixed points of a semigroup-nonexpensive mappings in Hilbert spaces. The method is a combination of projection, extragradient-Armijo algorithms and Manns method. We obtain a strong convergence for the sequences generated by the proposed method.

• 대한수학회지
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• 제58권3호
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• pp.525-552
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• 2021

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.665-732
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• 2015

Existence results for multiple positive solutions of two classes of boundary value problems for bilateral difference systems are established by using a fixed point theorem under convenient assumptions. It is the purpose of this paper to show that the approach to get positive solutions of boundary value problems of finite difference equations by using multi-fixed-point theorems can be extended to treat the bilateral difference systems with one-dimensional Laplacians. As an application, the sufficient conditions are established for finding multiple positive homoclinic solutions of a bilateral difference system. The methods used in this paper may be useful for numerical simulation. An example is presented to illustrate the main theorems. Further studies are proposed at the end of the paper.