• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.59-68
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• 2009

In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.441-464
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• 2010

In this paper, we introduce an iterative method for finding common elements of the set of solutions to a general system of variational inequalities for inverse-strongly accretive mappings and of the set of fixed points of strict pseudo-contractions in a real Banach space. The results presented in this paper mainly improve and extend the corresponding results announced by many others.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.19-35
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• 2017

In this communication, we introduce an Ishikawa type iterative algorithm for finding the approximate solutions of a class of nonlinear set valued variational inclusion problems. We also establish a characterization of strong convergence of this iterative techniques.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.237-245
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• 1997

The fixed point index plays an important role in solving the positive solutions of nonlinear equations in ordered Banach spaces ([7], [10], [11], [14], [15]). Many authors have studied the existence problems of positive solutions of nonlinear equations for nonlinear mappings ([1]-[5], [7], [9], [10], [14], [15]).

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.267-281
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• 2004

In this paper, we establish almost stability of Ishikawa iterative schemes with errors for the classes of Lipschitz $\phi$-strongly quasi-accretive operators and Lipschitz $\phi$-hemicontractive operators in arbitrary Banach spaces. The results of this paper extend a few well-known recent results.

• East Asian mathematical journal
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• v.14 no.1
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• pp.77-98
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• 1998

The purpose of this paper is to introduce and study the semigroups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, we utilize these results to study the Cauchy problem for a kind of differential inclusions with accertive mappings in probabilistic normed spaces.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.237-251
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• 2006

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.427-441
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• 2010

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

• East Asian mathematical journal
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• v.4
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• pp.129-137
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• 1988