Copyright © 2010 Lu-Chuan Ceng et al. This is an open access article distributed under the
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Let be a real Banach space with the dual space . Let be a proper functional and let be a bifunction. In this paper, a new concept of -proximal mapping of with respect to is introduced. The existence and Lipschitz continuity of the -proximal mapping of with respect to are proved. By using properties of the -proximal mapping of with respect to , a generalized mixed equilibrium problem with perturbation (for short, GMEPP) is introduced and studied in Banach space . An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space , and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in a Hilbert space.