• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.477-485
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• 1997

Let E be a smooth Banach space. Suppose T:$E \rightarrow E$ is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and ishikawa iteration methods), under suitable conditions converges strongly to a solution of the equation $T_x=f$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.79-91
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• 2010

In this paper, a class of fractional integrodifferential equations of mixed type with nonlocal conditions is considered. First, using contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. Second, the existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with nonlocal conditions is also presented.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.587-600
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• 2016

We obtain the general solution of the functional equation $f(ax+y)-f(x-ay)+{\frac{1}{2}}a(a^2+1)f(x-y)+(a^4-1)f(y)={\frac{1}{2}}a(a^2+1)f(x+y)+(a^4-1)f(x)$ and prove the stability problem of the quartic Lie ${\ast}$-derivation by using a directed method and an alternative fixed point method.

• 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.

• 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.

• 대한수학회보
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• 제51권3호
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• pp.621-640
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• 2014

In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

• 대한수학회보
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• 제46권6호
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• pp.1175-1188
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• 2009

In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of parametric generalized nonlinear mixed quasi-variational inclusions with (A, ${\eta$)-accretive mappings in quniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.129-141
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• 2018

In this slush pile, we introduce a new kind of variational inclusions problem stated as random extended generalized nonlinear variational inclusions for random fuzzy mappings. We construct an iterative scheme for the this variational inclusion problem and also discuss the existence of random solutions for the problem. Further, we show that the approximate solutions achieved by the generated scheme converge to the required solution of the problem.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권3호
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• pp.231-247
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• 2010

In this paper, we investigate the generalized Hyers-Ulam stability of a bi-Jensen functional equation $4f(\frac{x\;+\;y}{2},\;\frac{z\;+\;w}{2})$ = f(x, z) + f(x, w) + f(y, z) + f(y, w). Also, we establish improved results for the stability of a bi-Jensen equation on the punctured domain.

• 호남수학학술지
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• 제26권4호
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• pp.391-399
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• 2004

In this paper, we develop an iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities in Hilbert spaces. The resolvent operator technique is used to establish the equivalence between variational inequalities and fixed point problems. This equivalence is used to study the existence of a solution of nonlinear mixed implicit variational inequalities and to suggest an iterative algorithm for solving variational inequalities. In our results, we do not assume that the mapping is strongly monotone.