Fixed Point for Almost Contractions in v-Generalized b-Metric Spaces

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Kadyan A., Rathee S., Kumar A., Rani A., Tas K.

Fractal and Fractional, vol.7, no.1, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.3390/fractalfract7010060
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Keywords: b-metric spaces, generalized metric spaces, v-generalized b-metric spaces
  • Uşak University Affiliated: Yes

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.