Meir-Keeler Contraction In RectangularM−Metric Space

In this paper, we establish some fixed point theorems for a Meir-Keeler type contraction in M-metric spaces via Gupta-Saxena type contraction. Also, we extend and improve very recent results in fixed point theory.

Fixed Point Theory and Applications, 2013

Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013), we establish some common fixed point theorems for three and four self-mappings satisfying generalized Meir-Keeler α-contraction in metric spaces. As a consequence, the results of Rao and

Fixed Point Theory and Applications, 2015

In this paper, following the idea of Samet et al. (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52:156-158, 1984). As an application we derive some fixed points of mappings of integral type.

Fixed Point Theory and Applications, 2016

In this paper, we introduce the notion of generalized Meir-Keeler contraction mappings in the setup of b-metric-like spaces. Then we establish some fixed point results for this class of contractions. We also provide some examples to verify the effectiveness and applicability of our main results.

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.

Symmetry

In this article, we prove fixed point results for a Meir–Keeler type contraction due to orthogonal M-metric spaces. The results of the paper improve and extend some recent developments in fixed point theory. The extension is assured by the concluding remarks and followed by the main theorem. Finally, an application of the main theorem is established in proving theorems for some integral equations and integral-type contractive conditions.

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.

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

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.

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.