fixed point theorems for generalized orthogonal f-contraction and f-expansion of wardowski kind via the notion of ψ−fixed point

In this manuscript, we introduce generalized orthogonal (f∗, ψ)-contraction of kind (s) and use this concept to establish ψ-fixed point theorems in the frame of o-complete orthogonal metric space. secondly, we introduce the new notion of generalized orthogonal (f∗, ψ) expansive mapping and utilize the same to prove some fixed point results for surjective mapping satisfying certain conditions. our results extend and improve the results of [3] and [7] by omitting the continuity condition of f ∈ ℑ with the aid of ψ-fixed point. we also give an illustrative example which yields the main result. also, many existing results in the frame of metric spaces are established.