scholarly journals Wardowski Type Contractions and the Fixed-Circle Problem on S-Metric Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Nabil Mlaiki ◽  
Ufuk Çelik ◽  
Nihal Taş ◽  
Nihal Yilmaz Özgür ◽  
Aiman Mukheimer
Keyword(s):  
Metric Space ◽  
Common Property ◽  
Metric Spaces ◽  
The Self ◽  
Circle Problem ◽  
The Common

In this paper, we present new fixed-circle theorems for self-mappings on an S-metric space using some Wardowski type contractions, ψ-contractive, and weakly ψ-contractive self-mappings. The common property in all of the obtained theorems for Wardowski type contractions is that the self-mapping fixes both the circle and the disc with the center x0 and the radius r.

COMMON FIXED POINT THEOREM FOR TWO MAPPINGS IN bi-b-METRIC SPACE

2022 ◽  
Vol 11 (1) ◽  
pp. 25-34
Author(s):  
V.D. Borgaonkar ◽  
K.L. Bondar ◽  
S.M. Jogdand
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Common ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Unique Common Fixed Point

In this paper we have used the concept of bi-metric space and intoduced the concept of bi-b-metric space. our objective is to obtain the common fixed point theorems for two mappings on two different b-metric spaces induced on same set X. In this paper we prove that on the set X two b-metrics are defined to form two different b-metric spaces and the two mappings defined on X have unique common fixed point.

scholarly journals Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Akbar Azam ◽  
Jamshaid Ahmad ◽  
Cristina Di Bari
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Generalized Contraction ◽  
Complex Valued Metric Space ◽  
The Common ◽  
Complex Valued ◽  
Common Coupled Fixed Points ◽  
Coupled Fixed Points

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

scholarly journals Fixed-disc results on metric spaces

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 447-457
Author(s):  
Nihal Taş ◽  
Nabil Mlaiki ◽  
Hassen Aydi ◽  
Nihal Özgür
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Geometric Properties ◽  
Circle Problem ◽  
Fixed Point Techniques

In this paper, we deal with the geometric properties of non-unique fixed points for self-mappings of a metric space (resp. an S-metric space). The fixed-disc (resp. fixed-circle) problem has been investigated in this setting. To obtain new fixed-disc results, we modify some known fixed-point techniques. Illustrative examples are also given to show the validity of our main results.

Some Recent Developments in theory of Metric Spaces

2021 ◽  
Vol 23 (07) ◽  
pp. 1314-1320
Author(s):  
Parveen Sheoran ◽  
Keyword(s):  
Topological Space ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Scalar Function ◽  
Distinct Advantage ◽  
Daily Lives ◽  
Recent Developments ◽  
Common Concept ◽  
The Common

The topology on a set X is formed by a non-negative real valued scalar function called metric, which may be understood as measuring some quantity. Because some of the set’s attributes are similar, there’s a distance between any two elements, or points. Quite evocative of the common concept of distance that we come across in our daily lives. Because its topology is entirely defined by a scalar distance function, this sort of topological space has a distinct advantage over all others. We may reasonably assume that we are familiar with the qualities of such a function and are capable of dealing with it successfully. Instead, a generic topology is frequently dictated by a set of perhaps abstract rules. Frecklet initially proposed the concept of a metric space in 1906, but it was Hausdorff who coined the phrase metric space a few years later.

scholarly journals On the Fixed-Circle Problem and Khan Type Contractions

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 80 ◽  
Author(s):  
Nabil Mlaiki ◽  
Nihal Taş ◽  
Nihal Özgür
Keyword(s):  
Open Problem ◽  
Metric Spaces ◽  
Circle Problem ◽  
The Common

In this paper, we consider the fixed-circle problem on metric spaces and give new results on this problem. To do this, we present three types of F C -Khan type contractions. Furthermore, we obtain some solutions to an open problem related to the common fixed-circle problem.

scholarly journals Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 58 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
The Self ◽  
Complete Metric Spaces

In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

scholarly journals Using the Supremum Form of Auxiliary Functions to Study the Common Coupled Coincidence Points in Fuzzy Semi-Metric Spaces

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 5
Author(s):  
Hsien-Chung Wu
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Points ◽  
Coupled Coincidence Points ◽  
Cauchy Sequences ◽  
The Common ◽  
Rational Condition ◽  
Common Coupled Fixed Points ◽  
Coupled Coincidence ◽  
Coupled Fixed Points

This paper investigates the common coupled coincidence points and common coupled fixed points in fuzzy semi-metric spaces. The symmetric condition is not necessarily satisfied in fuzzy semi-metric space. Therefore, four kinds of triangle inequalities are taken into account in order to study the Cauchy sequences. Inspired by the intuitive observations, the concepts of rational condition and distance condition are proposed for the purpose of simplifying the discussions.

scholarly journals A general lemma for fixed-point theorems involving more than two maps inD-metric spaces with applications

2003 ◽  
Vol 2003 (11) ◽  
pp. 661-672
Author(s):  
B. C. Dhage ◽  
Smrati Arya ◽  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
General Lemma ◽  
The Common ◽  
Common Fixed Point Theorems

A general procedural lemma for fixed-point theorems for three and four maps in aD-metric space is proved, and it is further applied for proving the common fixed-point theorems of three and four maps in aD-metric space satisfying certain contractive conditions.

Approximate Fixed Point Sequences of Nonlinear Semigroups in Metric Spaces

2015 ◽  
Vol 58 (2) ◽  
pp. 297-305 ◽  
Author(s):  
M. A. Khamsi
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Ishikawa Iteration ◽  
Nonlinear Semigroups ◽  
Approximate Fixed Point ◽  
Nonexpansive Semigroups ◽  
The Family ◽  
The Common ◽  
Nonlinear Mappings

AbstractIn this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings {T1}t≥0, i.e., a family such that T0(x) = x, Ts+t = Ts(Tt(x)), where the domain is a metric space (M; d). In particular, we prove that under suitable conditions the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings.

scholarly journals COMMUNAL FIXED POINT IN FUZZY 2- METRIC SPACES

2021 ◽  
Vol 7 (7) ◽  
pp. 481-487
Author(s):  
Atianashie Miracle A ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Compatible Mappings ◽  
The Common ◽  
Common Fixed Point Theorem

The objective of this paper is to emphasize the Common Fixed Point in Fuzzy 2- Metric Spaces and prove a common fixed point theorem of compatible mappings of type (R) in fuzzy 2-metric space. We consider four mappings of which one is continuous. The results generalize many results in the literature. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and the degree of utility of our results.

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