On Orthogonal Interpolative Iterative Mappings with Applications in Multiplicative Calculus

Abstract

In this paper, we report orthogonal interpolative versions of some
celebrated iterative mappings. We provide various concrete conditions on the
real valued functions J , S : (0, infinity) to  R for the existence of fixed-points
of (J , S)-orthogonal interpolative terative mappings. We obtain many fixed
point theorems in orthogonal multiplicative metric spaces. We apply (J, S)
interpolative version of Banach fixed point theorem to show the existence of so-
lutions to multiplicative integral equation and fractional differential equation.
We support the reported theory with non-trivial examples.