Let E be a real uniformly convex and uniformly smooth Banach space with the dual space E∗. Let J:E→E∗ be the normalized duality mapping and A:E→2^{E∗} a maximal \eta-relaxed monotone mapping. The purpose of this article is two fold. First we present the characterizations of \eta-relaxed monotone mappings on uniformly convex and uniformly smooth Banach spaces, and also some properties of the resolvent mapping associated with maximal \eta-relaxed monotone mapping are proved. Secondly, iterative algorithms for approximating a common element of the set of fixed points of nonlinear mapping and the set of solution of variational inclusion problems involving maximal \eta-relaxed mappings is proposed, and then strong convergence theorems are proved. The results improve and extend some recent results in the literature.

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