scholarly journals Some Noncontractive Maps on Incomplete Metric Spaces Have Also Fixed Points

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Tawseef Rashid ◽  
Qamrul Haq Khan ◽  
Nabil Mlaiki ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
The Given

In this article, we discuss a new version of metric fixed point theory. The application of this newly introduced concept is to find some fixed point results where many well-known results in literature cannot be applied. We give some examples to illustrate the given concepts and obtained results.

scholarly journals Fixed Points of g-Interpolative Ćirić–Reich–Rus-Type Contractions in b-Metric Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 132
Author(s):  
Youssef Errai ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Type ◽  
The Given ◽  
Type Contraction

We use interpolation to obtain a common fixed point result for a new type of Ćirić–Reich–Rus-type contraction mappings in metric space. We also introduce a new concept of g-interpolative Ćirić–Reich–Rus-type contractions in b-metric spaces, and we prove some fixed point results for such mappings. Our results extend and improve some results on the fixed point theory in the literature. We also give some examples to illustrate the given results.

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 On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

scholarly journals Common fixed point results for generalized (ψ,β)-geraghty contraction type mapping in partially ordered metric-like spaces with application

Filomat ◽  
2017 ◽  
Vol 31 (17) ◽  
pp. 5497-5509 ◽  
Author(s):  
Habes Alsamir ◽  
Mohd Noorani ◽  
Wasfi Shatanawi ◽  
Kamal Abodyah
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Partial Metric ◽  
Partially Ordered ◽  
Partial Metric Spaces ◽  
Contraction Type

Harandi [A. A. Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 2012 (2012), 10 pages] introduced the notion of metric-like spaces as a generalization of partial metric spaces and studied some fixed point theorems in the context of the metric-like spaces. In this paper, we utilize the notion of the metric-like spaces to introduce and prove some common fixed points theorems for mappings satisfying nonlinear contractive conditions in partially ordered metric-like spaces. Also, we introduce an example and an application to support our work. Our results extend and modify some recent results in the literature.

scholarly journals On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2048
Author(s):  
Jelena Vujaković ◽  
Eugen Ljajko ◽  
Slobodan Radojević ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Approach ◽  
Complete Metric Spaces

Many authors used the concept of F−contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

scholarly journals Fixed Points of Eventually Δ-Restrictive and Δ(ϵ)-Restrictive Set-Valued Maps in Metric Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 127 ◽  
Author(s):  
Pradip Debnath ◽  
Manuel de La Sen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Intrinsic Property ◽  
Point Theory ◽  
Symmetry Principles ◽  
Definition Of ◽  
Metric Function

The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually Δ -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the Δ ( ϵ ) -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples.

scholarly journals On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhilong Li ◽  
Shujun Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Partial Order ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Monotone Mappings ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Minimal Fixed Point

We presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.

scholarly journals Existence and uniqueness of the solutions of some classes of integral equations C*-algebra-valued b-metric spaces

2020 ◽  
Vol 68 (4) ◽  
pp. 726-742
Author(s):  
Esad Jakupović ◽  
Hashem Masiha ◽  
Zoran Mitrović ◽  
Seyede Razavi ◽  
Reza Saadati
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Point Theory ◽  
C Algebra ◽  
Coupled Fixed Points

Introduction/purpose: The aim of the paper is to establish some coupled fixed point results in C*-algebra-valued b-metric spaces. Moreover, the obtained results are used to define the sufficient conditions for the existence of the solutions of some classes of integral equations. Methods: The method of coupled fixed points gives the sufficient conditions for the existence of the solution of some classes of integral equations. Results: New results were obtained on coupled fixed points in C*-algebra-valued b-metric space. Conclusion: The obtained results represent a contribution in the fixed point theory and open new possibilities of application in the theory of differential and integral equations.

Fixed point problems concerning contractive type operators on KST-Spaces

2018 ◽  
Vol 34 (3) ◽  
pp. 287-294
Author(s):  
ARSLAN H. ANSARI ◽  
◽  
LILIANA GURAN ◽  
ABDUL LATIF ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fixed Point Problems ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Contractive Type

In this paper, using the concept of w-distance we prove some results on the existence of fixed points for contractive type operators, namely; (α, µ)-ψ-contractive operators. Applications are also presented. Our results improve and generalize a number of known results of fixed point theory including the recent results of Guran and Bota [ Guran, L. and Bota, M.-F., Ulam-Hyers Stability Problems for Fixed Point Theorems concerning α-ψ-Type Contractive Operators on KST-Spaces, Submitted in press.] and Ansari [Ansari, A. H. and Shukla, S., Some fixed point theorems for ordered F-(F, h)-contraction and subcontractions in θ-f-orbitally complete partial metric spaces, J. Adv. Math. Stud., 9 (2016), No. 1, 37–53].

scholarly journals On Convergence of Fixed Points in Fuzzy Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yonghong Shen ◽  
Dong Qiu ◽  
Wei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Research Direction ◽  
Point Theory ◽  
Fuzzy Metric Spaces ◽  
Contraction Mappings ◽  
Fuzzy Metric

We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.

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