Ishikawa type iterative algorithm for completely generalized nonlinear quasi-variational-like inclusions in Banach spaces
In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for compuiing their approximate solutions by applying the new notion of J(eta)-proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in Banach spaces, Appl. Math. Comput. 163 (2005) 295-308]. We prove that the approximate solutions obtained by the proposed algorithm converge to the exact solution of our quasi-variational-like inclusions. The results presented in this paper extend and improve the corresponding results of [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in Banach spaces, Appl. Math. Comput. 163 (2005) 295-308; X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369-383; N.J. Huang, Generalized nonlinear variational inclusions with non-compact valued mappings, Appl. Math. Lett. 9(3) (1996) 25-29; A. Hassouni, A. Moudafi, A perturbed algorithm for variational inclusions, J. Math. Anal. Appl. 185(3) (1994) 706-712]. Some special cases are also discussed. (c) 2006 Elsevier Ltd. All rights reserved.
algorithm quasi-variational-like inclusions ishikawa iterative sequence reflexive banach spaces proximal mapping