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 Applications of Fixed Point Theory in Integral Equations and Homotopy Using Partially Ordered S_b Metric Spaces

2018 ◽  
Vol 7 (3.3) ◽  
pp. 146 ◽  
Author(s):  
D Ram Prasad ◽  
GNV Kishore ◽  
K Priyanka
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Homotopy Theory ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Partially Ordered

In this paper we give some applications to integral equations as well as homotopy theory via Suzuki  type fixed point theorems in partially ordered complete  - metric space by using generalized contractive conditions. We also furnish an example which supports our main result.  

scholarly journals Relation-Theoretic Fixed Point Theorems for Generalized Weakly Contractive Mappings

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 29
Author(s):  
Priyam Chakraborty ◽  
Binayak S. Choudhury ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Other ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Fixed Point Result ◽  
Weakly Contractive

In recent times there have been two prominent trends in metric fixed point theory. One is the use of weak contractive inequalities and the other is the use of binary relations. Combining the two trends, in this paper we establish a relation-theoretic fixed point result for a mapping which is defined on a metric space with an arbitrary binary relation and satisfies a weak contractive inequality for any pair of points whenever the pair of points is related by a given relation. The uniqueness is obtained by assuming some extra conditions. The metric space is assumed to be R -complete. We use R -continuity of functions. The property of local T-transitivity of the relation R is used in the main theorem. There is an illustrative example. An existing fixed point result is generalized through the present work. We use a method in the proof of our main theorem which is a blending of relation-theoretic and analytic approaches.

scholarly journals Fixed Point Theory of Weak Contractions in Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
Jin-Chirng Lee ◽  
Chao-Hung Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

We prove two new fixed point theorems in the framework of partially ordered metric spaces. Our results generalize and improve many recent fixed point theorems in the literature.

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 Quadruple Fixed Point Theorems in Partially Ordered Metric Spaces Depending on Another Function

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hassen Aydi ◽  
Erdal Karapınar ◽  
İlker Şavas Yüce
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Quadruple Fixed Point

We prove quadruple fixed point theorems in partially ordered metric spaces depending on another function. Also, we state some examples showing that our results are real generalization of known ones in quadruple fixed point theory.

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.

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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