H-Mixed Accretive Mapping and Proximal Point Method for Solving a System of Generalized Set-Valued Variational Inclusions
Mohd Iqbal Bhat, Sumeera Shafi, Mudasir Malik · Numerical Functional Analysis and Optimization · 2021
In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving αβ-H((.,.),(.,.))-mixed accretive mapping in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm for finding the approximate solution of the system. Furthermore, we prove that the sequences generated by the iterative algorithm converge strongly to a solution of the system.