Convergence and stability of iterative algorithms of generalized set-valued variational-like inclusions in Banach spaces K.R. Kazmi * , M.I. Bhat Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India Abstract In this paper, we give the notion of P-g-proximal mapping, an extension of P-prox- imal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous g-subdifferentiable proper functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a class of gener- alized set-valued variational-like inclusions in Banach space and show its equivalence with a class of implicit Wiener–Hopf equations using the concept of P-g-proximal map- ping. Using this equivalence, we propose a new class of iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the exist- ence of solution of generalized set-valued variational-like inclusions and discuss the con- vergence criteria and the stability of the iterative algorithm. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Generalized set-valued variational-like inclusion; P-g-proximal mapping, Iterative algorithm; Implicit Wiener–Hopf equation; Convergence criteria; Stability 0096-3003/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2004.04.057 * Corresponding author. E-mail addresses: krkazmi0@postmark.net (K.R. Kazmi), iqbal92@math.com (M.I. Bhat). Applied Mathematics and Computation 166 (2005) 164–180 www.elsevier.com/locate/amc