A system of generalized variational inclusions involving generalized H(·, ·)-accretive mapping in real q-uniformly smooth Banach spaces |
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Authors: | KR Kazmi FA KhanMohammad Shahzad |
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Institution: | a Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India b Department of Mathematics, Faculty of Science, Tabuk University, Tabuk 71491, Saudi Arabia c Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202002, India |
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Abstract: | In this paper, we consider a class of accretive mappings called generalized H(·, ·)-accretive mappings in Banach spaces. We prove that the proximal-point mapping of the generalized H(·, ·)-accretive mapping is single-valued and Lipschitz continuous. Further, we consider a system of generalized variational inclusions involving generalized H(·, ·)-accretive mappings in real q-uniformly smooth Banach spaces. Using proximal-point mapping method, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions. Furthermore, we discuss the convergence criteria of the iterative algorithm under some suitable conditions. Our results can be viewed as a refinement and improvement of some known results in the literature. |
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Keywords: | System of generalized variational inclusions Generalized H(· · )-accretive mapping Proximal-point mapping method Iterative algorithm Convergence criteria |
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