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1. On the Convergence of a Parallel Iterative Algorithm for Two Finite Families of Uniformly L-Lipschitzian Mappings.

Author

FENG GU

Subjects
*STOCHASTIC convergence, *ITERATIVE methods (Mathematics), *MATHEMATICAL mappings, *BANACH spaces, *ALGORITHMS, *CONVEX sets
Abstract

In this paper, we study a necessary and sufficient condition for the strong convergence of a parallel iterative algorithm for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by S. S. Chang, Y. J. Cho, E. U. Ofoedu, J. Schu, L. C. Zeng and many others. [ABSTRACT FROM AUTHOR]

Published
2011

2. A New System of Nonlinear Variational Inclusions with (Ai, ηi)-Accretive Operators in Banach Spaces.

Author

FENGRONG ZHANG, ZEQING LIU, SHIN MIN KANG, and YOUNG CHEL KWUN

Subjects
*BANACH spaces, *VECTOR spaces, *GENERALIZED spaces, *STOCHASTIC convergence, *ALGORITHMS, *MATHEMATICAL sequences
Abstract

In this paper, we introduce and study a new system of nonlinear variational inclusions with (A,η)-accretive operators in Banach spaces. Using the resolvent operator technique associated with (A,η)-accretive operator, we prove the existence and uniqueness of solutions for the system of nonlinear variational inclusions, construct a Mann iterative algorithm with errors for solving the system of nonlinear variational inclusions and discuss the convergence of the iterative sequence generated by the algorithm. [ABSTRACT FROM AUTHOR]

Published
2012

3. Convergence Theorems on an Iterative Method for Variational Inequality Problems and Fixed Point Problems.

Author

Xiaolong Qin and Shin Min Kang

Subjects
*ITERATIVE methods (Mathematics), *FIXED point theory, *STOCHASTIC convergence, *VISCOSITY, *APPROXIMATION theory, *MATHEMATICAL inequalities, *NONEXPANSIVE mappings, *HILBERT space, *ALGORITHMS
Abstract

In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of xed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. [ABSTRACT FROM AUTHOR]

Published
2010