scholarly journals Discontinuity at fixed point and metric completeness

2020 ◽  
Vol 21 (2) ◽  
pp. 349
Author(s):  
Ravindra K. Bisht ◽  
Vladimir Rakocevic
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Open Problem ◽  
Fixed Point Theorems ◽  
Intersection Property ◽  
Contractive Mappings

<p>In this paper, we prove some new fixed point theorems for a generalized class of Meir-Keeler type mappings, which give some new solutions to the Rhoades open problem regarding the existence of contractive mappings that admit discontinuity at the fixed point. In addition to it, we prove that our theorems characterize completeness of the metric space as well as Cantor's intersection property.</p>

scholarly journals Caristi type and meir-keeler type fixed point theorems

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3711-3721 ◽  
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
M.C. Joshi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Intersection Property ◽  
Contractive Mappings ◽  
Contractive Type

We generalize the Caristi fixed point theorem by employing a weaker form of continuity and show that contractive type mappings that satisfy the conditions of our theorem provide new solutions to the Rhoades? problem on continuity at fixed point. We also obtain a Meir-Keeler type fixed point theorem which gives a new solution to the Rhoades? problem on the existence of contractive mappings that admit discontinuity at the fixed point. We prove that our theorems characterize completeness of the metric space as well as Cantor?s intersection property.

scholarly journals On ParametricS-Metric Spaces and Fixed-Point Type Theorems for Expansive Mappings

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Nihal Taş ◽  
Nihal Yılmaz Özgür
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Point Type

We introduce the notion of a parametricS-metric space as generalization of a parametric metric space. Using some expansive mappings, we prove a fixed-point theorem on a parametricS-metric space. It is important to obtain new fixed-point theorems on a parametricS-metric space because there exist some parametricS-metrics which are not generated by any parametric metric. We expect that many mathematicians will study various fixed-point theorems using new expansive mappings (or contractive mappings) in a parametricS-metric space.

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 The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

scholarly journals Common Fixed Point Theorems for Nonlinear Contractive Mappings in Dislocated Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yijie Ren ◽  
Junlei Li ◽  
Yanrong Yu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mapping Theorem ◽  
Contractive Mappings ◽  
Dislocated Metric Space ◽  
Common Fixed Point Theorems ◽  
Dislocated Metric

In 1986, Matthews generalized Banach contraction mapping theorem in dislocated metric space that is a wider space than metric space. In this paper, we established common fixed point theorems for a class of contractive mappings. Our results extend the corresponding ones of other authors in dislocated metric spaces.

scholarly journals Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jamshaid Ahmad ◽  
Chakkrid Klin-Eam ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

scholarly journals Some Fixed Point Theorems of Contractive Mappings in P b r -Cone Metric Spaces over Banach Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abba Auwalu ◽  
Evren Hinçal
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Contractive Mappings ◽  
Cone Metric

In this paper, we introduce the concept of a P b r -cone metric space over Banach algebras and prove some fixed point results under various contractive mappings in such a space. Some examples are given to elucidate the results. Our results extend and generalize many existing results in the literature.

scholarly journals Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

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