Extended b-metric space, extended b-comparison function and nonlinear contractions

Fagin et al. used some kind of relaxed triangle inequality for the distance measure in pattern matching and called this measure as non-linear elastic matching. Intrigued by such idea, recently, Kamran et al. introduced a new intuitive concept of distance measure to extend the notion of b-metric space. We present some fixed point theorems when the underlying ambient space is an extended b-metric space and the contraction condition involve a new class of comparison functions. To substantiate the validity of our results we obtain many well-known pre-existing results in literature. Moreover, we have applied our result to study the solution to an integral equation. © 2018, Politechnica University of Bucharest. All rights reserved.