Sumeera Shafi - Department of Mathematics, S.P. College, Cluster University, Srinagar-۱۹۰۰۰۱, India.

A system of generalized mixed variational inclusion problem (SGMVIP) is considered involving H(.,.)-mixed mappings in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, the existence of solution of this system of variational inclusions is given. A new two-step iterative algorithm is proposed for solving SGMVIP. Strong convergence of the proposed algorithm is given.

System of generalized mixed variational inclusion problem, H(. , .)-mixed mappings, Proximal-point mapping