Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space

In this work, we introduce a new class of self-maps which satisfy the (E.A.) property with respect to some q∈M, where M is q-starshaped subset of a convex metric space and common fixed point results are established for this new class of self-maps. After that we obtain some invariant approximation results as an application. Our results represent a very strong variant of the several recent results existing in the literature. We also provide some illustrative examples in the support of proved results.