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 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 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 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 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.

scholarly journals Double Controlled Partial Metric Type Spaces and Convergence Results

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Haroon Ahmad ◽  
Mudasir Younis ◽  
Mehmet Emir Köksal
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Metric ◽  
Numerical Examples ◽  
Convergence Results ◽  
Partial Metric Spaces ◽  
Type Spaces ◽  
Theoretical Results

In this paper, we firstly propose the notion of double controlled partial metric type spaces, which is a generalization of controlled metric type spaces, partial metric spaces, and double controlled metric type spaces. Secondly, our aim is to study the existence of fixed points for Kannan type contractions in the context of double controlled partial metric type spaces. The proposed results enrich, theorize, and sharpen a multitude of pioneer results in the context of metric fixed point theory. Additionally, we provide numerical examples to illustrate the essence of our obtained theoretical results.

scholarly journals The Pb-cone metric spaces over Banach algebra with applications

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 983-998
Author(s):  
Jerolina Fernandez ◽  
Neeraj Malviya ◽  
Diana Dolicanin-Dekic ◽  
Dzenis Pucic
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Banach Algebras ◽  
Point Theory ◽  
Nonlinear Integral Equations ◽  
Cone Metric Spaces ◽  
Lipschitz Mappings ◽  
Partial Cone ◽  
Uniqueness Of A Solution ◽  
Cone Metric

The aim of the article is to establish the structure of partial cone b-metric spaces over Banach algebras. Topological and structural properties are investigated of the new spaces. We also define generalized Lipschitz mappings and give their application in fixed point theory. The results presented in this paper substantially extend and strengthen the results of the literature. Few examples are provided to support our conclusions and as an application we establish the existence and uniqueness of a solution to a class of system of nonlinear integral equations.

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