ITERATIVE ALGORITHM FOR A SYSTEM OF MULTI-VALUED VARIATIONAL INCLUSIONS INVOLVING $(B, \phi)$-MONOTONE MAPPINGS IN BANACH SPACES

Authors

  • K. Kazmi Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
  • N. Ahmad Department of Mathematics, P.O. Box 2014, Skaka, Al-Jouf University, Kingdom of Saudi Arabia

Abstract

In this paper, we introduce a new class of resolvent mappings for $(B, \phi)$-monotone mappings in Banach space, which is a natural and important generalization of a class of resolvent mappings studied in [X.-P. Luo, N.-J. Huang; A new class of variational inclusions with B-monotone operators in Banach spaces, J. Comput. Appl. Math. 233 (2010), 1888-1896]. We study some properties of this new class of resolvent mappings and by making use of it, we discuss the existence and iterative approximation of solutions of a system of multi-valued variational inclusions. The method and results presented in this paper improve and generalize many known results in the literature.

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Published

2012-03-31

How to Cite

Kazmi, K., & Ahmad, N. (2012). ITERATIVE ALGORITHM FOR A SYSTEM OF MULTI-VALUED VARIATIONAL INCLUSIONS INVOLVING $(B, \phi)$-MONOTONE MAPPINGS IN BANACH SPACES. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 3(1), 13-23. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/99

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Section

Research Article