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 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 suggestaniterativealgorithmforthesystemofgeneralizedvariationalinclusionsundersomesuitableconditions.Further,wediscusstheconvergenceofiterativealgorithm usingtheconceptofgraphconvergence.Ourresultscanbeviewedasarefinement andgeneralizationofsomeknownresultsintheliterature.

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