scholarly journals Some Fixed Point Results of Weak-Fuzzy Graphical Contraction Mappings with Application to Integral Equations

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 541
Author(s):  
Shamoona Jabeen ◽  
Zhiming Zheng ◽  
Mutti-Ur Rehman ◽  
Wei Wei ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Continuity Condition ◽  
Graph Structure ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Cone Metric

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory.

scholarly journals On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhilong Li ◽  
Shujun Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Partial Order ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Monotone Mappings ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Minimal Fixed Point

We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

scholarly journals Remarks on fixed point theory in soft metric type spaces

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5531-5541 ◽  
Author(s):  
Mujahid Abbas ◽  
Ghulam Murtaza ◽  
Salvador Romaguera
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Type Spaces ◽  
Cone Metric

The aim of this paper is to discuss the recent development regarding fixed point theory in soft metric type spaces such as soft G-metric spaces, soft cone metric spaces, dislocated soft metric spaces and soft b-metric spaces. We show that soft versions of fixed point results proved in such metric type spaces can be directly deduced from the comparable existing results in the literature.

scholarly journals Generalized distances and their associate metrics. Impact on fixed point theory

2013 ◽  
Vol 22 (1) ◽  
pp. 23-32
Author(s):  
VASILE BERINDE ◽  
◽  
MITROFAN CHOBAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Cone Metric Spaces ◽  
Generalized Metric Spaces ◽  
Partial Metric Spaces ◽  
Cone Metric

In the last years there is an abundance of fixed point theorems in literature, most of them established in various generalized metric spaces. Amongst the generalized spaces considered in those papers, we may find: cone metric spaces, quasimetric spaces (or b-metric spaces), partial metric spaces, G-metric spaces etc. In some recent papers [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799-1803], [Haghi, R. H., Rezapour, Sh. and Shahzad, N., Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454], [Samet, B., Vetro, C. and Vetro, F., Remarks on G-Metric Spaces, Int. J. Anal., Volume 2013, Article ID 917158, 6 pages http://dx.doi.org/10.1155/2013/917158], the authors pointed out that some of the fixed point theorems transposed from metric spaces to cone metric spaces, partial metric spaces or G-metric spaces, respectively, are sometimes not real generalizations. The main aim of the present note is to inspect what happens in this respect with b-metric spaces.

scholarly journals Coupled fixed point analysis in fuzzy cone metric spaces with an application to nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Gui-Xiu Chen ◽  
Shamoona Jabeen ◽  
Saif Ur Rehman ◽  
Ahmed Mostafa Khalil ◽  
Fatima Abbas ◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Contraction Mappings ◽  
Point Analysis ◽  
Cone Metric

AbstractIn this paper, we introduce the concept of coupled type and cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. We establish some coupled fixed point results without the mixed monotone property, and also present some coupled fixed results using the partial order metric in the said space. We present some strong coupled fixed point theorems using cyclic coupled type fuzzy cone contraction mappings in fuzzy cone metric spaces. Moreover, we present an application of nonlinear integral equations for the existence of a unique solution to support our work.

scholarly journals On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Fixed Point Properties ◽  
Contractive Maps

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

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