scholarly journals Fixed point theorems via w-distance in relational metric spaces with an application

Filomat ◽  
2020 ◽  
Vol 34 (6) ◽  
pp. 1889-1898
Author(s):  
Gopi Prasad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Binary Relation ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
First Order ◽  
Contractive Mappings

In this paper, we establish fixed point theorems for generalized nonlinear contractive mappings using the concept of w-distance on metric spaces endowed with an arbitrary binary relation. Our fixed point theorems generalize recent results of Senapati and Dey [ J. Fixed Point Theory Appl., 19, 2945-2961, (2017)] and many other important results of the existing literature. Moreover, in order to revel the usability of our findings an example and an application to first order periodic boundary value problem are given.

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

scholarly journals Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Lower Solution ◽  
Existence Of Solution ◽  
Order Ordinary Differential Equation ◽  
Complete Metric Spaces ◽  
First Order ◽  
Contractive Mappings

We establish a fixed point theorem withw-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

scholarly journals Related Fixed Point Theorems in Partially Ordered b -Metric Spaces and Applications to Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Paper ◽  
Point Theory ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Weakly Contractive

In this research paper, we have set some related fixed point results for generalized weakly contractive mappings defined in partially ordered complete b -metric spaces. Our results are an extension of previous authors who have already worked on fixed point theory in b -metric spaces. We state some examples and one sample of the application of the obtained results in integral equations, which support our results.

scholarly journals On modified α-Φ-asymmetric Meir-Keeler contractive mappings

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1855-1869 ◽  
Author(s):  
P. Salimi ◽  
N. Hussain ◽  
A. Roldan ◽  
E. Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Mappings ◽  
Nonlinear Anal

Samet et al. [Nonlinear Anal. 75:2154-2165, 2012] introduced and studied ?-?-contractive mappings. More recently Salimi, et al. [Fixed Point Theory Appl., 2013:151] modified the notion of ?-?-contractive mappings and improved the fixed point theorems in [20, 32]. Here we utilize these notions to establish fixed point results for modified ?-?-asymmetric Meir-Keeler contractions and triangular ?-admissible mappings defined on G-metric and cone G-metric spaces. Several interesting consequences of our theorems are also provided here to illustrate the usability of the obtained results.

Coincidence Theorems in New Generalized Metric Spaces Under Locally g-transitive Binary Relation

2018 ◽  
Vol 85 (3-4) ◽  
pp. 396
Author(s):  
Gopi Prasad ◽  
Ramesh Chandra Dimri
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Coincidence Theorems ◽  
Transitive Binary Relation

<p>In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].</p>

scholarly journals From graphical metric spaces to fixed point theory in binary related distance spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3209-3231 ◽  
Author(s):  
López Roldán ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Binary Relation ◽  
Directed Graph ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Transitive Relation ◽  
Ordered Metric Spaces

Very recently, many fixed point results have been introduced in the setting of graphical metric spaces. Due to their intimate links, such works also deal with metric spaces endowed with partial orders. As the reachability relationship in any directed graph (containing all cycles) is a reflexive transitive relation (that is, a preorder), but it is not necessarily a partial order, results on graphical metric spaces are independent from statements on ordered metric spaces. The main aim of this paper is to show that fixed point theorems in the setting of graphical metric spaces can be directly deduced from their corresponding results on measurable spaces endowed with a binary relation. Finally, we also describe the main advantages of involving this last class of spaces.

New fixed point results in bv(s)-metric spaces

2020 ◽  
Vol 70 (2) ◽  
pp. 441-452
Author(s):  
Tatjana Došenović ◽  
Zoran Kadelburg ◽  
Zoran D. Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Generalized Metric ◽  
The One

Abstract Z. D. Mitrović and S. Radenović introduced in [The Banach and Reich contractions in bv(s)-metric spaces, J. Fixed Point Theory Appl. 19 (2017), 3087–3095] a new class of generalized metric spaces and proved some fixed point theorems in this framework. The purpose of this paper is to consider other kinds of contractive mappings in bv(s)-metric spaces, and show how the work in the new settings differs from the one in standard metric and b-metric spaces. Examples show the usefulness of the obtained results.

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Common Fixed Point Theorems for Generalized Cyclic Contraction Pair in Partial B-Metric Spaces

2019 ◽  
Vol 8 (10S) ◽  
pp. 85-89
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of generalized cyclic contraction pair with transitive mapping in partial b-metric spaces. Also, we establish some fixed point theorems for this contraction pair. Our results generalize and improve the result of Oratai Yamaod, Wutiphol Sintunavarat and Yeol Je Cho (Fixed Point Theory App. 2015:164) in partial-b-metric spaces.

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