(H,ϕ)-η-Accretive Mappings and a New System of Generalized Variational Inclusions with(H,ϕ)-η-Accretive Mappings in Banach Spaces

摘要

We introduce a new class of generalized accretive mappings, named(H,ϕ)-η-accretive mappings, in Banach spaces. We define a resolvent operator associated with(H,ϕ)-η-accretive mappings and show its Lipschitz continuity. We also introduce and study a new systemof generalized variational inclusions with(H,ϕ)-η-accretive mappings in Banach spaces. By usingthe resolvent operator technique associated with(H,ϕ)-η-accretive mappings, we construct a newiterative algorithm for solving this system of generalized variational inclusions in Banach spaces. Wealso prove the existence of solutions for the generalized variational inclusions and the convergenceof iterative sequences generated by algorithm. Our results improve and generalize many knowncorresponding results.