On some recent coincidence and immediate consequences in partially ordered b-metric spaces

Abstract

The aim of this article is to present, improve and generalize some recent coincidence and coupled coincidence point results from several papers in the framework of partially ordered b-metric spaces. Two examples are also provided to support the superiority of the obtained results. MSC: 47H10; 54H25

On Coupled Common Fixed Point Theorems for Nonlinear Contractions with the Mixed Weakly Monotone Property in Partially OrderedS-Metric Spaces

“…On the other hand, several authors have studied fixed point theory in generalized metric spaces. For details, we refer readers to [8][9][10][11][12][13]. In 2012, Sedghi et al [14] have introduced the notion of an -metric space and proved that this notion is a generalization of a metric space.…”

Some coincidence point results for T-contraction mappings on partially ordered b-metric spaces and applications to integral equations

“…The purpose of this paper is to state some fixed point results for T -contractive mappings in partially ordered b-metric spaces that generalize the main results of [10]. As an application, we discuss the existence for a solution of a nonlinear integral equation.…”

“…Now we shall give some notions used in the next section. These notions are generalizations of notions introduced in [10].…”

“…(i) The pair (f, g) is called h-compatible if lim n→∞ d(f hgx n , ghf x n ) = 0 whenever {x n } is a sequence in X such that lim n→∞ hf x n = lim n→∞ hgx n = t for some t ∈ X. If we choose hx = x for all x ∈ X, then the pair (f, g) is called compatible [10]. If we choose gx = x for all x ∈ X, then f is called h-compatible.…”

Fixed point results for admissible mappings with application to integral equations

“…So far numerous authors have focused on fixed point results in b-metric spaces (see [1,6,[17][18][19][20]). …”