On orthogonal interpolative iterative mappings with applications in multiplicative calculus

In this paper, some orthogonal interpolative versions of celebrated iterative mappings are reported. Various concrete conditions on the real valued functions T, S : (0, infinity) -> (-infinity, infinity) for the existence of fixed-points of (T, S)-orthogonal interpolative iterative mappings are studied. We obtain fixed point theorems for Kannan type, Chatterjea type, Ciric-Reich-Rus type and Hardy-Rogers type (T, S)-contractions via interpolation in orthogonal multiplicative metric space. The fixed point theorem for Banach (T, S)orthogonal contraction via interpolation is applied to show the existence of solutions to integral equation and fractional differential equation. The reported theory is supported by non-trivial examples.