An extension of Karapinar and Sadaranganis’ result through the C-class functions by using α-admissible mapping with applications

The main objective of this work is to introduce a new type non-linear contraction via C-class functions by using ?-admissible mapping. Our results extend and generalize the very recent Karapinar Sadarangani (2015. RACSAM. [37]). Illustrative examples are given support our findings. We have shown that satisfy periodic fixed point after modifying contraction. Next, we findings from self-mapping T two self-mappings T; S. Also, an example provided justify effectiveness result on self mappings, where partially ordered structure fails. Finally, apply solve ordinary differential integral equations.