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Mathematical Problems in Engineering
Volume 2015, Article ID 408165, 9 pages
http://dx.doi.org/10.1155/2015/408165
Research Article

Solving Split Variational Inclusion Problem and Fixed Point Problem for Nonexpansive Semigroup without Prior Knowledge of Operator Norms

School of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, China

Received 5 July 2015; Accepted 19 October 2015

Academic Editor: Fabio Tramontana

Copyright © 2015 Haitao Che and Meixia Li. 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 an iterative method to approximate a common solution of split variational inclusion problem and fixed point problem for nonexpansive semigroups with a way of selecting the stepsizes which does not need any prior information about the operator norms in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge strongly to a common element of the set of solutions of a split variational inclusion and the set of common fixed points of one-parameter nonexpansive semigroups. Moreover, numerical results demonstrate the performance and convergence of our result, which may be viewed as a refinement and improvement of the previously known results announced by many other researchers.