Strong convergence of an iterative scheme for accretive operators in Banach spaces

Renu Chugh, Rekha Rani

Abstract


In 2009, Kumam [7] introduced a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for monotone, Lipschitz-continuous mappings and proved its strong convergence in a real Hilbert space. The aim of this paper is to prove a strong convergence result of this iterative scheme in the setting of Banach spaces involving an inverse strongly accretive operator under some conditions. As a special case, we shall prove that proposed iterative scheme converges strongly to minimum norm solution of some variational inequality problem.

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Published: 2017-01-02

How to Cite this Article:

Renu Chugh, Rekha Rani, Strong convergence of an iterative scheme for accretive operators in Banach spaces, Advances in Inequalities and Applications, Vol 2017 (2017), Article ID 5

Copyright © 2017 Renu Chugh, Rekha Rani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Inequalities and Applications

ISSN 2050-7461

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