Some fixed point theorems for expansiveness of orthogonal $p$-contractiveness

Orthogonal set and orthogonal metric spaces are two new notions, which are defined in 2017. In this type metric spaces, a generalization of Banach fixed point theorem is presented. Then in 2019, new fixed point theorems are investigated by using altering distance functions. In this paper, fixed point theorems for expansiveness of orthogonal $p$-contractiveness via altering distance functions are given inspired by [Rhoades B.E. Some theorems on weakly contractive maps. Nonlinear Anal. 2001, 47 (4), 2683$-$2693] and [Gordji M.E., Rameani M., De La Sen M., Cho Y.J. On orthogonal sets and Banach fixed point theorem. Fixed Point Theory 2017, 18 (2), 569$-$578]. Further, consequences and a restrictive example are offered.