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 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 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 Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

scholarly journals Meir-Keeler Contraction In Rectangular M−Metric Space

2021 ◽  
Vol 9 (1) ◽  
pp. 96-104
Author(s):  
Mohammad Asim ◽  
Samad Mujahid ◽  
Izhar Uddin
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Type Contraction

Abstract In this paper, we prove some fixed point theorems for a Meir-Keeler type Contraction in rectangular M−metric space. Thus, our results extend and improve very recent results in fixed point theory.

scholarly journals Pseudo Picard operators on generalized metric spaces

2018 ◽  
Vol 12 (2) ◽  
pp. 389-400 ◽  
Author(s):  
Ishak Altun ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
New Class ◽  
Generalized Metric

In this paper, we present a new class of pseudo Picard operators in the setting of generalized metric spaces introduced recently in [M. Jleli and B. Samet: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., (2015) 2015:61]. An example is provided to illustrate the main result.

scholarly journals On Best Proximity Points under the -Property on Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Point Of View ◽  
Ordered Metric Spaces

Very recently, Abkar and Gabeleh (2013) observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property) can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.

scholarly journals Fixed Point Theorems on Generalized Rectangular Metric Spaces

2021 ◽  
Vol 65 (1) ◽  
pp. 59-84
Author(s):  
O. K. Adewale ◽  
◽  
J. O. Olaleru ◽  
H. Olaoluwa ◽  
H. Akewe
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Rectangular Metric Space

In this paper, we introduce the notion of generalized rectangular metric spaces which extends rectangular metric spaces introduced by Branciari. Analogues of the some well-known fixed point theorems are proved in this space. With an example, it is shown that a generalized rectangular metric space is neither a G-metric space nor a rectangular metric space. Our results generalize many known results in fixed point theory.

scholarly journals Unification of the Fixed Point in Integral Type Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 732 ◽  
Author(s):  
Panda Kumari ◽  
Badriah Alamri ◽  
Nawab Hussain ◽  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Integral Type ◽  
Predominant Role

In metric fixed point theory, the conditions like “symmetry” and “triangle inequality” play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary.

A Study on Fixed Point Theory in M-Metric Space

2020 ◽  
Vol 13 (13) ◽  
pp. 62-68
Author(s):  
Prakash Muni Bajracharya ◽  
Nabaraj Adhikari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Partial Metric Space ◽  
Point Theory ◽  
Partial Metric ◽  
The Fixed Point Theorem

In 2014, Asadi et al.1 introduced the notion of an M−metric space which is the generalization of a partial metric space and establish Banach and Kannan fixed point theorems in M− metric space. In this paper, we give a brief survey regarding the fixed point theorem for Chatterjea contraction mapping in the framework of M−metric space. We also give some examples which support the partial answers to the question posed by Asadi et al. concerning a fixed point for Chatterjea contraction mapping.

scholarly journals Some fixed point results for rational type and subrational type contractive mappings

2017 ◽  
Vol 9 (1) ◽  
pp. 185-201
Author(s):  
Huaping Huang ◽  
Arslan Hojat Ansari ◽  
Diana Dolićanin-Đekić ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Mappings ◽  
Rational Type

Abstract In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97). Moreover, we give an example to support our results.

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