Some fixed point results based on contractions of new types for extended $b$-metric spaces

The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $b$-metric spaces in the sense introduced by Kamran et al. [A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $b$-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.