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 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 Cyclic generalized φ-contractions in b-metric spaces and an application to integral equations

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2047-2057 ◽  
Author(s):  
Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Problem ◽  
Contractive Mappings

We introduce the notion of cyclic generalized ?-contractive mappings in b-metric spaces and discuss the existence and uniqueness of fixed points for such mappings. Our results generalize many existing fixed point theorems in the literature. Examples are given to support the usability of our results. Finally, an application to existence problem for an integral equation is presented.

scholarly journals A Fixed Point Theorem for Contractive Mappings with Nonlinear Combinations of Rational Expressions in b-Metric Spaces

2017 ◽  
Vol 58 (1) ◽  
pp. 29-46
Author(s):  
W. E. Barrera ◽  
J. R. Morales ◽  
E. M. Rojas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Distance Functions ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Rational Expressions ◽  
Rational Type

AbstractIn this paper we discuss the existence and uniqueness of fixed points for mappings satisfying several (nonlinear-combinations) contractive inequalities of rational type controlled by altering distance functions. Our results extend several fixed point results in the literature.

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 Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Marin Borcut ◽  
Mădălina Păcurar ◽  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Nonlinear Mappings

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.

scholarly journals Discussion onα-ψContractions on Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We discuss the existence and uniqueness of fixed points ofα-ψcontractive mappings in complete generalized metric spaces, introduced by Branciari. Our results generalize and improve several results in the literature.

scholarly journals FIXED POINTS OF ALMOST GENERALIZED $(\alpha,\beta)$-$(\psi, \varphi)$-CONTRACTIVE MAPPINGS IN $b$-METRIC SPACES

2018 ◽  
Vol 33 (2) ◽  
pp. 177
Author(s):  
Gutti Venkata Ravindranadh Babu ◽  
Tolera Mosissa Dula
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Contractive Maps ◽  
Alpha Beta

In this paper, we introduce almost generalized $(\alpha,\beta)$-$(\psi, \varphi)$-contractive maps, and we prove some new xed point results for this class of mappings in b-metric spaces. We provide examples in support of our results. Our results extend/generalize the results of Dutta and Choudhury [8] and Yamaod and Sintunavarat [13].

Sign in / Sign up

Export Citation Format

Share Document