Geraghty Type Generalized F-Contractions and Related Applications in Partial b-Metric Spaces

Abstract

The purpose of this paper is to introduce new concepts of(α,β)-admissible Geraghty type generalizedF-contraction and to prove that some fixed point results for such mappings are in the perspective of partialb-metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphicF-contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partialb-metric space. Moreover, some examples are presented to illustrate the usability of the new theory.

Some applications of fixed point results for generalized two classes of Boyd–Wong’s F-contraction in partial b-metric spaces

“…Very recently, Piri et al [9] improve the result of Wardowski [7] by launching the concept of an F-Suzuki contraction and proved some curious fixed point results. The results of Wardowski [7] were generalized by several authors (see, e.g., [10][11][12][13][14] ).…”

Meir–Keeler Fixed-Point Theorems in Tripled Fuzzy Metric Spaces

“…Later, George and Veeramani [14] gave a necessary and sufficient condition for the completeness of fuzzy metric space. Since then, various fixed-point results for mappings satisfying different contractive conditions were established by many researchers [15][16][17][18][19][20][21]. Moreover, in 2019, Zheng and Wang [22] proposed the concept of fuzzy Meir-Keeler contractive mappings in fuzzy metric spaces, which covers fuzzy ψ-contractive mappings and fuzzy H-contractive mappings in [23,24] as special cases, and obtained some Meir-Keeler-type fixed-point theorems.…”

Some ϕ-fixed point results in b-metric spaces with applications

“…The Banach contraction principle is one of the most important subjects in mathematics. By using this principle, most authors have proved several fixed point theorems for various mappings in several metric spaces [1][2][3]5,6,[8][9][10][11][16][17][18][19][20][21][22][23]. Bakhtin [12] and Czerwik [21] introduced b-metric spaces as a generalization of metric spaces and proved the contraction mapping principle in b-metric spaces that is an extension of the Banach contraction principle in metric spaces.…”