Common fixed points of generalized Meir-Keeler α-contractions

International Journal of Mathematics and Mathematical Sciences, 1993

In this paper, we introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. Our result extends, generalized and improves some results of Meir-Keeler, Park-Bae, Park-Rhoades, Pant and Rao-Rao, etc. 1991 AMS SUBJECT CLASSIFICATION CODE. 54H25.

Journal of Ultra Scientist of Physical Sciences Section A, 2018

In this paper, we establish some fixed point theorems using Meir-Keeler type contraction in M-metric spaces via Gupta-Saxena type contraction. We also extend very recent results in fixed point theory.

2020

The purpose of this work is to introduce the notion of a multivalued strictly (α, β)-admissible mappings and a multivalued (α, β)-Meir-Keeler contractions with respect to the partial Hausdorff metric Hp in the framework of partial metric spaces. In addition, we present fixed points and endpoints results for a multivalued (α, β)-Meir-Keeler contraction mappings in the framework of the complete partial metric spaces. The results obtained in this work provides extension as well as substantial generalizations and improvements of several well-known results on fixed point theory and its applications. MSC: 47H09; 47H10; 49J20; 49J40

Filomat, 2014

In this paper, we extend a recent Meir-Keeler type fixed point theorem of Suzuki (2008) to a pair of maps on a metric space.

Nepal Journal of Science and Technology, 1970

The theory of fixed point is a very extensive field, which has various applications. The present paper deals with some developments of Meir-Keeler type fixed point theorem as its remarkable generalizations under several contractive definitions in metric space.Key words: Common fixed point; Contraction; Metric space; Compatible mapsDOI: 10.3126/njst.v10i0.2956Nepal Journal of Science and Technology Vol. 10, 2009 Page: 141-147

In this paper, we introduce a new type of a generalized-(α, ψ)-Meir-Keeler contractive mapping and establish some interesting theorems on the existence of fixed points for such mappings via admissible mappings. Applying our results, we derive fixed point theorems in ordinary metric spaces and metric spaces endowed with an arbitrary binary relation. MSC: 47H10; 54H25

In this paper, first we introduce the notion of a G m -Meir-Keeler contractive mapping and establish some fixed point theorems for the G m -Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G m c -Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(α, ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces. MSC: 46N40; 47H10; 54H25; 46T99 theorems for the G m -Meir-Keeler contractive mapping in the setting of G-metric spaces. In Section , we introduce the notion of a G m c -Meir-Keeler contractive mapping in the setting of cone G-metric spaces and establish a fixed point result. Later, we introduce the notion of a G-(α, ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.

Fixed Point Theory and Applications, 2012

In this paper we introduce generalized symmetric Meir-Keeler contractions and prove some coupled fixed point theorems for mixed monotone operators F : X × X → X in partially ordered metric spaces. The obtained results extend, complement and unify some recent coupled fixed point theorems due to Samet [B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508-4517], Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393] and some other very recent papers. An example to show that our generalizations are effective is also presented.

m-hikari.com

We introduced a general class of contraction maps on a metric space, called Acontractions (that includes the contractions originally studied by R. Kannan, M. S. Khan at el, R. Bianchini, and S. Reich), and extended some common fixed point theorems on M. S. Khan's contractions to general self maps of a metric space satisfying certain A-contraction type condition; in this paper, we prove exact analogues of these results in the setting of generalized metric spaces (defined originally by A. Branciari).

Fixed Point Theory and Applications, 2013

In this paper, first we introduce the notion of a G m -Meir-Keeler contractive mapping and establish some fixed point theorems for the G m -Meir-Keeler contractive mapping in the setting of G-metric spaces. Further, we introduce the notion of a G m c -Meir-Keeler contractive mapping in the setting of G-cone metric spaces and obtain a fixed point result. Later, we introduce the notion of a G-(α, ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces. MSC: 46N40; 47H10; 54H25; 46T99 theorems for the G m -Meir-Keeler contractive mapping in the setting of G-metric spaces. In Section , we introduce the notion of a G m c -Meir-Keeler contractive mapping in the setting of cone G-metric spaces and establish a fixed point result. Later, we introduce the notion of a G-(α, ψ)-Meir-Keeler contractive mapping and prove some fixed point theorems for this class of mappings in the setting of G-metric spaces.

Advances in Fixed Point Theory, 2016

In this paper, we introduce a new class Ψ1 of functions which are different from Ψ introduced by Hussain, Parvaneh, Samet and Vetro [9]. We define JS - Ψ1 - contraction for a single selfmap and prove the existence of fixed points. Also, we extend JS - Ψ1 - contraction to a pair of selfmaps and prove the existence of coincidence points and prove the existence of common fixed points by assuming the weakly compatible property. Further, we study the existence of common fixed points for a pair of weakly compatible selfmaps satisfying property (E. A). Examples are provided to illustrate our results.

Applied General Topology

In this paper, we introduce the notions of generalized α-F-contraction and modified generalized α-F-contraction. Then, we present sufficient conditions for existence and uniqueness of fixed points for the above kind of contractions. Necessarily, our results generalize and unify several results of the existing literature. Some examples are presented to substantiate the usability of our obtained results.

Journal of Function Spaces

We present a fixed point theorem for generalized (α,ψ)-Meir-Keeler type contractions in the setting of generalized b-metric spaces. The presented results improve, generalize, and unify many existing famous results in the corresponding literature.

Tamkang Journal of Mathematics, 2004

The purpose of this paper is two fold. In the following pages we prove common fixed point theorems for four mappings $ A$, $B$, $S$ and $ T $ (say) under the Meir-Keeler type $ (\varepsilon, \delta) $ condition, however, without imposing any additional condition on $delta$ or using a $ \phi $-contractive condition together with. Simultaneously we also show that none of the $ A $, $ B $, $ S $ or $ T $ is continuous at their common fixed point. Thus we not only generalize the Meir-Keeler type and Boyd-Wong type fixed point theorems, but also provide one more answer to the problem (see Rhoades [19]) on the existence of a contractive definition, which is strong enough to generate a fixed point but does not force the map to be continuous at the fixed point.

Acta Mathematica Scientia, 2012

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.