scholarly journals Fixed Points of Contractive Mappings inb-Metric-Like Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Nawab Hussain ◽  
Jamal Rezaei Roshan ◽  
Vahid Parvaneh ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Periodic Point ◽  
Topological Structure ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Different Types ◽  
Convergence Of Sequences

We discuss topological structure ofb-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results inb-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results.

scholarly journals Extended partial b-metric spaces and some fixed point results

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2837-2850 ◽  
Author(s):  
V. Parvaneh ◽  
Z. Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Volterra Type ◽  
Fundamental Lemma ◽  
Contractive Mappings ◽  
Type Integral ◽  
Convergence Of Sequences ◽  
Weakly Contractive

In this paper, we introduce the concept of extended partial b-metric space. We demonstrate a fundamental lemma for the convergence of sequences in such spaces. Then we prove some fixed point results for weakly contractive mappings in the setup of ordered extended partial b-metric spaces. An example is given to verify the effectiveness and applicability of our main results. An application of these results to Volterra-type integral equations is provided at the end.

A Remark on Contractive Mappings

1970 ◽  
Vol 13 (1) ◽  
pp. 111-113 ◽  
Author(s):  
Kai-Wang Ng
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Periodic Point ◽  
Metric Space ◽  
Contractive Mappings

Much current research is concerned with the fixed points of contractive mappings (mappings which shrink distance in some manner) from a metric space into itself. In this remark we shall point out that most mappings treated in the literature are very special in the sense that all these mappings satisfy a condition which is rather severe: every periodic point must necessarily be a fixed point.

scholarly journals Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Poom Kumam ◽  
Calogero Vetro ◽  
Francesca Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Partial Metric ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Partial Metric Spaces

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

scholarly journals Fixed Points of ModifiedF-Contractive Mappings in Complete Metric-Like Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Erdal Karapınar ◽  
Hossein Piri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Related Literature ◽  
Contractive Mappings

We introduce the notion of modifiedF-contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature.

scholarly journals Fixed Point Of Contractive Mappings Of Integral Type Over An S^{JS}- Metric Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Kushal Roy ◽  
Mantu Saha ◽  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Integral Type ◽  
Couple Fixed Point ◽  
Contractive Mappings

We obtain sufficient conditions for existence of fixed points of integral type contractive mappings on an S^{JS}- metric spaces. We also study common fixed point and couple fixed point of integral type mappings and construct examples to support our results.

scholarly journals Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
Shahnaz Jafari ◽  
Maryam Shams ◽  
Asier Ibeas ◽  
Manuel De La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Linear Combination ◽  
Metric Space ◽  
Metric Spaces ◽  
Probabilistic Metric Space ◽  
Probabilistic Metric Spaces ◽  
Contractive Mappings ◽  
Probabilistic Metric ◽  
Infinite Linear

In this paper, we introduce the concept of enhanced probabilistic metric space (briefly EPM-space) as a type of probabilistic metric space. Also, we investigate the existence of fixed points for a (finite or infinite) linear combination of different types of contractive mappings in EPM-spaces. Furthermore, we investigate about the convergence of sequences (generated by a finite or infinite family of contractive mappings) to a common fixed point. The useful application of this research is the study of the stability of switched dynamic systems, where we study the conditions under which the iterative sequences generated by a (finite or infinite) linear combination of mappings (contractive or not), converge to the fixed point. Also, some examples are given to support the obtained results. In the end, a number of figures give us an overview of the examples.

scholarly journals On contractive mappings and discontinuity at fixed points

2020 ◽  
Vol 14 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Hiranmoy Garai ◽  
Lakshmi Dey ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces ◽  
Contractive Mappings ◽  
Interesting Open Problem

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

scholarly journals Results in Strongly Minihedral Cone and Scalar Weighted Cone Metric Spaces and Applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anita Tomar ◽  
Meena Joshi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Negative Answer ◽  
Contractive Condition ◽  
Natural Question ◽  
Cone Metric Spaces ◽  
Convergence Of Sequences ◽  
Cone Metric

Abstract The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly mini-hedral cone, and scalar weighted cone assuming the cone to be strongly mini-hedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.

scholarly journals Common Fixed Points for Weakψ-Contractive Mappings in Ordered Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sumit Chandok ◽  
Simona Dinu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Contractive Mappings ◽  
Common Fixed Point Theorems

We obtain some new common fixed point theorems satisfying a weak contractive condition in the framework of partially ordered metric spaces. The main result generalizes and extends some known results given by some authors in the literature.

scholarly journals Periodic Points and Fixed Points for the Weaker(ϕ,φ)-Contractive Mappings in Complete Generalized Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Chi-Ming Chen ◽  
W. Y. Sun
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Periodic Points ◽  
Generalized Metric Spaces ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of weaker(ϕ,φ)-contractive mapping in complete metric spaces and prove the periodic points and fixed points for this type of contraction. Our results generalize or improve many recent fixed point theorems in the literature.

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