A new approach in the context of ordered incomplete partial b-metric spaces

The main purpose of this paper is to find some fixed point results with a new approach, particularly in those cases where the existing literature remains silent. More precisely, we introduce partial completeness, f-orbitally completeness, a new type of contractions and many other notions. We also ensure the existence of fixed points for non-contraction maps in the class of incomplete partial b-metric spaces. We have reported some examples in support of our results. 2020 Tawseef Rashid et al., published by De Gruyter 2020.The publication of this article was funded by the Qatar National Library. The authors highly appreciate the efforts of referees and editor of this paper who helped us to improve it in several places.Scopu

A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation

A Relation-Theoretic Metrical Fixed Point Theorem for Rational Type Contraction Mapping with an Application

In this article, we discuss the relation theoretic aspect of rational type contractive mapping to obtain fixed point results in a complete metric space under arbitrary binary relation. Furthermore, we provide an application to find a solution to a non-linear integral equation

Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions

We prove some coincidence theorems involving a pair of self-mappings f and g defined on an ordered metric space X wherein f is g-increasing φ-contractive mapping. In our results, neither the whole space X nor the range subspaces (f(X) or g(X)) are required to be complete. Instead, we use the completeness of a subspace of X satisfying suitable conditions

On Prešić–Ćirić-Type α-ψ Contractions with an Application

In this paper, we extend the idea of α-ψ contraction mapping to the product spaces by introducing Prešić–Ćirić-type α-ψ contractions and utilize them to prove some coincidence and common fixed-point theorems in the context of ordered metric spaces using α-admissibility of the mapping. Our newly established results generalize a number of well-known fixed-point theorems from the literature. Moreover, we give some examples that attest to the credibility of our results. Further, we give an application to the nonlinear integral equations, which can be employed to study the existence and uniqueness of solutions to the integral equations

On Prešić–Ćirić-Type <i>α</i>-<i>ψ</i> Contractions with an Application

In this paper, we extend the idea of α-ψ contraction mapping to the product spaces by introducing Prešić–Ćirić-type α-ψ contractions and utilize them to prove some coincidence and common fixed-point theorems in the context of ordered metric spaces using α-admissibility of the mapping. Our newly established results generalize a number of well-known fixed-point theorems from the literature. Moreover, we give some examples that attest to the credibility of our results. Further, we give an application to the nonlinear integral equations, which can be employed to study the existence and uniqueness of solutions to the integral equations

Fixed Point Results Using Ft-Contractions in Ordered Metric Spaces Having t-Property

In this paper, we prove the existence of fixed points of F t -contraction mappings in partially ordered metric spaces not necessarily complete. We require that the ordered metric space has the t-property, which is a new concept introduced recently by Rashid et.al. We also give some examples to illustrate the new concepts and obtained results