Fixed Point for Almost Contractions in <i>v</i>-Generalized <i>b</i>-Metric Spaces

Abstract

We present a significant example to show that the class of v-generalized b-metric spaces properly contains the class of v-generalized metric spaces as well as b-metric spaces. This is accomplished because the example provided by Došenović et al. (2020) is insufficient to expose the generality of v-generalized b-metric spaces over the existing related spaces. Therefore, we establish fixed point theorems by defining generalized almost contractions of rational type and Reich type in v-generalized b-metric spaces. Moreover, we compare the proven results with the already existing fixed point theorems in this space by presenting suitable examples. As a consequence of these fixed point theorems, we further develop some common fixed-point results that ensure the existence and uniqueness of coincidence points and common fixed points for a pair of self maps. Finally, we use the outcome to check that the given Fredholm integral equation has a solution and that it is also unique.

Keywords

• <i>b</i>-metric spaces
• generalized metric spaces
• <i>v</i>-generalized <i>b</i>-metric spaces