Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings

Let E be a real normed linear space, K be a nonempty subset of E and T:K→E be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., F(T):={x∈K:Tx=x}≠Φ, and there exist x∗∈F(T) and a strictly increasing function Φ:[0,∞)→[0,∞), Φ(0)=0 such that for all x∈K, there exists j(x−x∗)∈J(x−x∗) such that 〈Tx−x∗,j(x−x∗)〉⩽‖x−x∗‖2−Φ(‖x−x∗‖).