An extension of Karapinar and Sadaranganis' result through the C-class functions by using $\alpha$-admissible mapping with applications

Abstract

This paper consists of five sections. In the second section, we extend the very recent results of Karapinar and Sadarangani (2015. RACSAM. \cite{ks2015}) through the C-class function by using $\alpha$-admissible mapping. We give examples to support our new findings. In section three, we have shown that our results satisfy the periodic fixed point results after modifying the contraction. In section four, we extend our main findings from a self-mapping $\mathcal{T}$ to two self-mappings $\mathcal{T}; \mathcal{S}$. Next, we produce an example to support our new result, where the partially ordered structure fails. In the last section, we apply our new findings to solve ordinary differential and non-linear integral equations.