Iterative approximation of a solution of multi-valued variational-like inclusion in Banach spaces: A P-eta-proximal-point mapping approach

作者：Kazmi K R^*; Khan F A

来源：Journal of Mathematical Analysis and Applications, 2007, 325(1): 665-674.

DOI：10.1016/j.jmaa.2006.02.013

• multi-valued variational-like inclusion
• P-eta-accretive mapping
• P-eta-proximal-point mapping
• iterative algorithm
• convergence analysis

In this paper, we introduce a class of P-eta-accretive mappings, an extension of eta-m-accretive mappings [C.E. Chidume, K.R. Kazmi, H. Zegeye, Iterative approximation of a solution of a general variational-like inclusion in Banach spaces, Int. J. Math. Math. Sci. 22 (2004) 1159-1168] and P-accretive mappings [Y.-P. Fang, N.-J. Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647-653], in real Banach spaces. We prove some properties of P-eta-accretive mappings and give the notion of proximal-point mapping, termed as P-eta-proximal-point mapping, associated with P-eta-accretive mapping. Further, using P-eta-proximal-point mapping technique, we prove the existence of solution and discuss the convergence analysis of iterative algorithm, for multi-valued variational-like inclusions in real Banach space. The theorems presented in this paper extend and improve many known results in the literature.

• 出版日期2007-1-1