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We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotonemappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibriumproblem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common elementin the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansivemapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The mainresults extend various results existing in the current literature

New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces