Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 635030 13 pages doi 2011 635030 Research Article Variational-Like Inclusions and Resolvent Equations Involving Infinite Family of Set-Valued Mappings Rais Ahmad and Mohd Dilshad Department of Mathematics Aligarh Muslim University Aligarh 202002 India Correspondence should be addressed to Rais Ahmad raisain_123@ Received 18 December 2010 Accepted 23 December 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 R. Ahmad and M. Dilshad. 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. We study variational-like inclusions involving infinite family of set-valued mappings and their equivalence with resolvent equations. It is established that variational-like inclusions in real Banach spaces are equivalent to fixed point problems. This equivalence is used to suggest an iterative algorithm for solving resolvent equations. Some examples are constructed. 1. Introduction The important generalization of variational inequalities called variational inclusions have been extensively studied and generalized in different directions to study a wide class of problems arising in mechanics optimization nonlinear programming economics finance and applied sciences and so forth see for example 1-7 and references theirin. The resolvent operator technique for solving variational inequalities and variational inclusions is interesting and important. The resolvent operator technique is used to establish an equivalence between variational inequalities and resolvent equations. The resolvent equation technique is used to develop powerful and efficient numerical techniques for solving various classes of variational inequalities inclusions and related optimization problems. In this paper we established a relationship between .
