Graph convergence for the H ⋅ , ⋅ Open image in new window-mixed mappingwith an application for solving the system of generalized variationalinclusionsReport as inadecuate




Graph convergence for the H ⋅ , ⋅ Open image in new window-mixed mappingwith an application for solving the system of generalized variationalinclusions - Download this document for free, or read online. Document in PDF available to download.

Fixed Point Theory and Applications

, 2013:304

Variational Analysis and Fixed Point Theory

Abstract

In this paper, we investigate a class of accretive mappings called the H ⋅ , ⋅ Open image in new window-mixed mappingsin Banach spaces. We prove that the proximal-point mapping associated with the H ⋅ , ⋅ Open image in new window-mixed mapping issingle-valued and Lipschitz continuous. Some examples are given to justify thedefinition of H ⋅ , ⋅ Open image in new window-mixed mapping.Further, a concept of graph convergence concerned with the H ⋅ , ⋅ Open image in new window-mixed mapping isintroduced in Banach spaces and some equivalence theorems betweengraph-convergence and proximal-point mapping convergence for the H ⋅ , ⋅ Open image in new window-mixed mappingssequence are proved. As an application, we consider a system of generalizedvariational inclusions involving H ⋅ , ⋅ Open image in new window-mixed mappingsin real q-uniformly smooth Banach spaces. Using the proximal-pointmapping method, we prove the existence and uniqueness of solution and suggest aniterative algorithm for the system of generalized variational inclusions.Furthermore, we discuss the convergence criteria for the iterative algorithmunder some suitable conditions.

MSC: 47J19, 49J40, 49J53.

Keywords H ⋅ , ⋅ Open image in new window-mixed mapping graph convergence proximal-point mapping method system of generalized variational inclusions iterative algorithm  Download fulltext PDF



Author: Shamshad Husain - Sanjeev Gupta - Vishnu Narayan Mishra

Source: https://link.springer.com/







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