Meir-Keeler Type Research Articles

Meir-Keeler Type Contractions for Tripled Fixed Points

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.

Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type

We establish fixed point theorems for mixed monotone operators of Meir-Keeler type on ordered Banach spaces through projective metric. As applications, we use the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for different classes of nonlinear problems which include two-order two-point boundary value problems and fourth-order two-point boundary value problems for elastic beam equations.

Fixed points for asymptotic contractions of integral Meir-Keeler type

In this paper we introduce the notion of asymptotic contraction of integral Meir-Keeler type on a metric space and we prove a theorem which ensures existence and uniqueness of fixed points for such contractions. This result generalizes some recent results in the literature.

Common fixed point theorems for contraction type mappings in partially ordered metric spaces

The purpose of this paper to present the common fixed point theorems for a stronger Meir-Keeler type mapping in partially ordered metric space. Our results generalize some recent results.

A generalization of the Meir–Keeler type contraction

In this paper, we prove a fixed point theorem which has applications on maps called T-contractions which include a class that satisfies the Meir–Keeler type contractive condition. We also present an example that illustrates that T-contractions are a natural extension of the Meir–Keeler type contraction.

A Meir-Keeler common type fixed point theorem on partial metric spaces

In this article, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a partial metric space satisfying a generalized Meir-Keeler type contractive condition. The presented theorem extends several well known results in literature.

Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings

The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.

Fixed point and common fixed point theorems for the Meir-Keeler type functions in cone ball-metric spaces

‎In this paper‎, ‎we define a new cone ball-metric and get fixed points and common fixed points for the Meir-Keeler type functions in cone ball-metric spaces‎.

New Meir‐Keeler Type Tripled Fixed‐Point Theorems on Ordered Partial Metric Spaces

In this paper, we prove some new Meir‐Keeler type tripled fixed‐point theorems on a partially ordered complete partial metric space. Also, as application, some results of integral type are given.

Coupled fixed point theorems for generalized Meir-Keeler contractions in ordered partial metric spaces

In this paper, we prove some coupled fixed point theorems satisfying a Meir-Keeler type contractive condition for mappings enjoying the mixed monotone property in ordered partial metric spaces.

Common fixed points in cone metric spaces for [formula omitted]-pairs

In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f - M K -pair mappings and f - C J M -pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfies a contractive condition of Meir–Keeler type. These results extend and generalize some recent results from the literature. To conclude the paper, we extend our main result to non-regular cone metric spaces by using the scalarization method of Du.

A Meir-Keeler type common fixed point theorem for four mappings

In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result general- izes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly compatibility property and replacing the com- pleteness of the space with a set of four alternative conditions for maps satisfying an implicit relation. Also, our result improves the main result of H. Bouhadjera, A. Djoudi.

Common fixed point theorems for a weaker Meir–Keeler type function in cone metric spaces

In this work, we define a weaker Meir–Keeler type function ψ : int P ∪ { 0 } → int P ∪ { 0 } in a cone metric space, and under this weaker Meir–Keeler type function, we show the common fixed point theorems of four single-valued functions in cone metric spaces.

Coupled fixed point theorems for a generalized Meir–Keeler contraction in partially ordered metric spaces

Let X be a non-empty set and F : X × X → X be a given mapping. An element ( x , y ) ∈ X × X is said to be a coupled fixed point of the mapping F if F ( x , y ) = x and F ( y , x ) = y . In this paper, we consider the case when X is a complete metric space endowed with a partial order. We define generalized Meir–Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir–Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393].

A common fixed point theorem for the weaker Meir–Keeler type function

In this paper, we define the weaker Meir–Keeler type function ψ : ℜ + → ℜ + , and under this weaker Meir–Keeler type function, we show a common fixed point theorem of two set-valued mappings in a complete metric space. Our results generalize the results of Zhang (2007) [1].

Fixed points of multifunctions on regular cone metric spaces

Each metric space is a regular cone metric space. We shall extend a result about Meir–Keeler type contraction mappings on metric spaces to regular cone metric spaces. Also, we shall give some results about fixed point of weakly uniformly strict p -contraction multifunctions on regular cone metric spaces.

Best Proximity Point Theorems for p-Cyclic Meir-Keeler Contractions

AbstractWe consider a contraction map "Equation missing" of the Meir-Keeler type on the union of p subsets "Equation missing", "Equation missing", of a metric space ("Equation missing") to itself. We give sufficient conditions for the existence and convergence of a best proximity point for such a map.

Fixed Point Theorems for a Weaker Meir-Keeler Type "Equation missing" -Set Contraction in Metric Spaces

AbstractWe define a weaker Meir-Keeler type function and establish the fixed point theorems for a weaker Meir-Keeler type "Equation missing"-set contraction in metric spaces.

Generalized contractions of Meir–Keeler type, endpoints, set-valued dynamical systems and generalized pseudometrics in uniform spaces

This paper gives the concepts of W -families of generalized pseudodistances, Φ -families of generalized gauge maps and set-valued dynamical systems of ( W ; Φ ) -contractions of Meir–Keeler type in Hausdorff complete uniform spaces and a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions. The definitions, the results and the method presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. The paper includes examples which show a fundamental difference between our results and the well-known ones.

The uniqueness of endpoints for set-valued dynamical systems of contractions of Meir–Keeler type in uniform spaces

In this paper, the concept of the set-valued dynamical systems of contractions of Meir–Keeler type in uniform spaces is introduced and conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions are established. The definition and the result presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our result and the well-known ones.