Some Fixed Point Theorems for Almost (GF; δb)-Contractions and Application

We propose a new notion of multi-valued almost (GF; δb)-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.