Graph Convergence for the H(·,·)-Co-accretive Mapping with an Application

In this paper, we introduce a concept of graph convergence for the H ( · , · ) -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the H ( · , · ) -co-accretive mapping. Further, we consider a system of generalized...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2015-10, Vol.38 (4), p.1481-1506
Main Authors: Ahmad, R., Akram, M., Dilshad, M.
Format: Article
Language:English
Subjects:
Acquisitions & mergers
Applications of Mathematics
Banach spaces
Convergence
Inclusions
Iterative algorithms
Mapping
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we introduce a concept of graph convergence for the H ( · , · ) -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the H ( · , · ) -co-accretive mapping. Further, we consider a system of generalized variational inclusions involving H ( · , · ) -co-accretive mapping in real q -uniformly smooth Banach spaces. Using resolvent operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions under some suitable conditions. Further, we discuss the convergence of iterative algorithm using the concept of graph convergence. Our results can be viewed as a refinement and generalization of some known results in the literature.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-014-0103-z