*Correspondence: [email protected] 1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract The notion of modular metric space, being a natural generalization of classical modulars over linear spaces, was recently introduced. In this paper, we introduce a generalized F-contr...

We show how some results of the theory of iterated function systems can be derived from the Tarski–Kantorovitch fixed–point principle for maps on partially ordered sets. In particular, this principle yields, without using the Hausdorff metric, the Hutchinson–Barnsley theorem with the only restriction that a metric space considered has the Heine–Borel property. As a by–product, we also obtain so...

Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how...

In this paper the authors prove existence, uniqueness and approximation of the solutions for initial value problems of nonlinear fractional differential equations with nonlocal conditions, using the operator theoretic technique in a partially ordered metric space. The main results rely on the Dhage iteration principle embodied in the recent hybrid fixed point theorem of Dhage (2014) in a partia...

let (x, d) be a compact metric space and f : x → x be a continuous map. consider the metric space (k(x),h) of all non empty compact subsets of x endowed with the hausdorff metric induced by d. let ¯ f : k(x) → k(x) be defined by ¯ f(a) = {f(a) : a ∈ a} . we show that block-coppels chaos in f implies block-coppels chaos in ¯ f if f is a bijection.

*Correspondence: [email protected] 4Department of Mathematics, Kyungnam University Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric space under Hardy-Rogers-type contractive condition. This result improves some recently obtained on...

Azam et al. [1] introduced the concept of complex-valued metric spaces and obtained sufficient conditions for the existence of common fixed points of a pair of contractive type mappings involving rational expressions. Subsequently, several authors have studied the existence and uniqueness of the fixed points and common fixed points of self-mappings in view of contrasting contractive conditions....

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

The existence of fixed point in partially ordered sets has been studied and investigated recently in 1–13 and references therein. Since the various contractive conditions are important in metric fixed point theory, there is a trend to weaken the requirement on contractions. Nieto and Rodrı́guez-López in 8, 10 used Tarski’s theorem to show the existence of solutions for fuzzy equations and fuzzy ...

The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice. 1. Background, Definitions and Summary of Results. Working in set theory without the axiom of choice we study the deductive strength of the assertion MP: Metric spaces are paracompact. (Definitions are given below.) MP was first proved i...