International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 22, Pages 1159-1168
doi:10.1155/S0161171204209395

Iterative approximation of a solution of a general variational-like inclusion in Banach spaces

C. E. Chidume,1 K. R. Kazmi,1,2 and H. Zegeye1

1The Abdus Salam International Centre for Theoretical Physics, Trieste 34100, Italy
2Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India

Received 29 September 2002

Copyright © 2004 C. E. Chidume et al. 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.

Abstract

We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors.