Weak Partial b-Metric Spaces and Nadler’s Theorem

Abstract

We study the notions of weak partial b-metric space and weak partial Hausdorff b-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial b-metric space by using weak partial Hausdorff b-metric spaces. A non-trivial example to show the validity of our result is given.Mathematics Subject Classification 2010: 55M20, 47H10

Common Fixed Point Theorem for Hybrid Pair of Mappings in a Generalized $(F,\xi,\eta)$-contraction in weak Partial $b$- Metric Spaces with an Application

“…In 2019, Kanwal et al [21] gave a generalized concept from weak partial metric space to weak partial bmetric space as follows:…”

“…In 2018, Beg and Pathak [8] proved Nadler's theorem on weak partial metric spaces with application to homotopy result. Later, in 2019, Kanwal et al [21] dene the notion of weak partial b-metric spaces and weak partial Hausdor b-metric spaces along with the topology of weak partial b-metric space. Moreover, they generalized Nadler's theorem using weak partial Hausdor b-metric spaces in the context of a weak partial b-metric space.…”

On Unique and Nonunique Fixed Points and Fixed Circles in M v b

“…Bakhtin [3], Branciari [4], Asadi et al [5], George et al [6], Mitrović and Radenović [7], Özgür et al [8], Karahan and Isik [9], and Asim et al [10] introduced the notions of a b-metric, a rectangular metric and a v-generalized metric, an M-metric, a rectangular b-metric, a b v ðsÞ-metric, a rectangular M-metric, a generalized p b v -partial metric, and an M v -metric, respectively. Further, one may also refer to Fernandez et al [11] and Kanwal et al [12,13] for work in N b -cone metric spaces over Banach algebra, orthogonal F -metric spaces, and weak partial b-metric spaces, respec-tively. One may allude to Kirk and Shahzed [14], to study in detail about the generalizations of the metric notion.…”

Common Fixed-Point Theorems of Generalizedψ,φ−Weakly Contractive Mappings inb−Metric-Like Spaces and Application

“…Fernandez et al [10] introduced the concept of N b -cone metric spaces over a Banach algebra as a generalization of N-cone metric spaces over a Banach algebra and b-metric spaces and studied some coupled common fixed-point theorems for generalized Lipschitz mappings in this framework. In 2019, Kanwal et al [11] generalized Nadler's theorem in weak partial b-metric space by using weak partial Hausdorff b-metric spaces. In 2020, Abbas et al [12] introduced the concepts of ψ-contraction and monotone ψ-contraction correspondence in fuzzy b-metric spaces and obtained fixed-point results for these contractive mappings.…”