Fixed points in C∗-algebra valued b-metric spaces endowed with a graph

2018 ◽  
Vol 68 (3) ◽  
pp. 639-654 ◽  
Author(s):  
Sushanta Kumar Mohanta
Keyword(s):  
Fixed Points ◽  
Unique Solution ◽  
Operator Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Contraction Mapping Theorem ◽  
C Algebra

Abstract We discuss the existence and uniqueness of fixed points for a self-mapping defined on a C∗-algebra valued b-metric space endowed with a graph. Our results extend and supplement several recent results in the literature. Some examples are provided to illustrate our results. Finally, as an application of G-contraction mapping theorem, existence of unique solution for a type of operator equation is given.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

scholarly journals Some Globally Stable Fixed Points in b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 555 ◽  
Author(s):  
Umar Batsari ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Points ◽  
Partial Order ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Continuous Mapping ◽  
Regularity Property ◽  
Contractive Mappings ◽  
Metric Function ◽  
Globally Stable

In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete b-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the b-metric function has the regularity property. Our results improve, and generalize some current results in the literature.

scholarly journals FIXED POINTS OF GENERALIZED (ALPHA, PSI,PHI)-CONTRACTIVE MAPS AND PROPERTY(P) IN S-METRIC SPACES

2021 ◽  
pp. 349
Author(s):  
Gutti Venkata Ravindranadh Babu ◽  
Leta Bekere Kumssa
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Contractive Maps ◽  
Satisfy Property

In this paper, we introduce generalized (alpha, psi,phi)-contractive maps and provethe existence and uniqueness of xed points in complete S-metric spaces. We alsoprove that these maps satisfy property (P). We discuss the importance of study of the existence of xed points in S-metric space rather than in the setting of metric space.The results presented in this paper extends several well known comparable results in metric and G-metric spaces. We provide example in support of our result.

scholarly journals Arbitrary binary relations, contraction mappings and b -metric spaces

2020 ◽  
Vol 72 (4) ◽  
pp. 565-574
Author(s):  
S. Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Binary Relations ◽  
Coincidence Points

UDC 517.9We prove some results on the existence and uniqueness of fixed points defined on a b -metric space endowed with an arbitrary binary relation.  As applications, we obtain some statements on coincidence points involving a pair of mappings.  Our results generalize, extend, modify and unify several well-known results especially those obtained by Alam and Imdad [J. Fixed Point Theory and Appl., <strong>17</strong>, 693–702 (2015); Fixed Point Theory, <strong>18</strong>, 415–432 (2017); Filomat, <strong>31</strong>, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory and Appl., <strong>12</strong>, 221–238 (2012)].  Also, we provide an example to illustrate the suitability of results obtained.

scholarly journals C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Congcong Shen ◽  
Lining Jiang ◽  
Zhenhua Ma
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
C Algebra ◽  
Uniqueness Of The Solution

We introduce the notion of the C⁎-algebra-valued G-metric space. The existence and uniqueness of some fixed-point theorems for self-mappings with contractive or expansive conditions on complete C⁎-algebra-valued G-metric spaces are proved. As an application, we prove the existence and uniqueness of the solution of a type of differential equations.

scholarly journals Fixed Points Results in G-Metric Spaces

2019 ◽  
Vol 32 (1) ◽  
pp. 142
Author(s):  
Salwa Salman Abed ◽  
Anaam Neamah Faraj ◽  
Anaam Neamah Faraj
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Closed Ball ◽  
Local Contraction

  In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

scholarly journals The Kannan Contraction Mapping Theorem for Composition Operators in Metric Spaces and Partially Ordered Metric Spaces

2019 ◽  
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Composition Operators ◽  
Contraction Mapping Theorem ◽  
Ordered Metric Spaces ◽  
Kannan Contraction

In this paper, fixed point theorems of the Kannan type are obtained in the setting of metric space and metric space endowed with partial order, respectively, for self-mappings that are composition operators.

On the existence of fixed points of two rational type contractions in a dislocated quasi multiplicative metric spaces and it's application

2017 ◽  
Vol 8 (1) ◽  
pp. 59
Author(s):  
Ahmed H. Soliman ◽  
M. A. Ahmed ◽  
A. M. Zidan
Keyword(s):  
Functional Equation ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Rational Contraction ◽  
Multiplicative Metric Spaces ◽  
Multiplicative Metric Space ◽  
Rational Type

In this work, firstly we establish the xed point point results for two rational contraction self-mappings on dislocated quasi multiplicative metric spaces (abbrev dq-multiplicative metric space). Finally in order to illustrate our results, we present the study about the existence and uniqueness of solutions of the functional equation.

scholarly journals Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

2019 ◽  
Vol 27 (1) ◽  
pp. 5-33 ◽  
Author(s):  
Hanan Alolaiyan ◽  
Basit Ali ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Hausdorff Distance ◽  
Existence And Uniqueness ◽  
Asymptotic Estimate ◽  
Metric Spaces ◽  
Multivalued Operators ◽  
Fixed Point Sets

Abstract The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.

scholarly journals MULTIDIMENSIONAL FIXED POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE WITH APPLICATION

2021 ◽  
pp. 919
Author(s):  
Amrish Handa
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contraction Mapping Principle ◽  
Uniqueness Of The Solution ◽  
Isotone Mappings

The main aim of this article is to study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under contraction mapping principle on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to an integral equation. The results we obtain generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

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