Modular Lipschitzian and Contractive Maps

2015 ◽  
pp. 1-15 ◽  
Author(s):  
Vyacheslav V. Chistyakov
Keyword(s):  
Contractive Maps

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].

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

scholarly journals ON FRACTIONAL DIFFERENTIAL INCLUSION PROBLEMS INVOLVING FRACTIONAL ORDER DERIVATIVE WITH RESPECT TO ANOTHER FUNCTION

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040002 ◽  
Author(s):  
SAMIHA BELMOR ◽  
F. JARAD ◽  
T. ABDELJAWAD ◽  
MANAR A. ALQUDAH
Keyword(s):  
Differential Inclusion ◽  
Fractional Order ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Research Work ◽  
Main Tool ◽  
Nonlinear Boundary Value Problems ◽  
Inclusion Problems ◽  
Contractive Maps ◽  
Fractional Differential

In this research work, we investigate the existence of solutions for a class of nonlinear boundary value problems for fractional-order differential inclusion with respect to another function. Endpoint theorem for [Formula: see text]-weak contractive maps is the main tool in determining our results. An example is presented in aim to illustrate the results.

scholarly journals A Completely Bounded Noncommutative Choquet Boundary for Operator Spaces

2017 ◽  
Vol 2019 (22) ◽  
pp. 6819-6886 ◽  
Author(s):  
Raphaël Clouâtre ◽  
Christopher Ramsey
Keyword(s):  
Structural Properties ◽  
Extension Property ◽  
Operator Space ◽  
Operator Spaces ◽  
Unique Extension ◽  
Bounded Linear ◽  
C Algebra ◽  
Choquet Boundary ◽  
Linear Maps ◽  
Contractive Maps

Abstract We develop a completely bounded counterpart to the noncommutative Choquet boundary of an operator space. We show how the class of completely bounded linear maps is too large to accommodate our purposes. To overcome this obstacle, we isolate the subset of completely bounded linear maps admitting a dilation of the same norm that is multiplicative on the associated C*-algebra. We view such maps as analogs of the familiar unital completely contractive maps, and we exhibit many of their structural properties. Of particular interest to us are those maps that are extremal with respect to a natural dilation order. We establish the existence of extremals and show that they have a certain unique extension property. In particular, they give rise to *-homomorphisms that we use to associate to any representation of an operator space an entire scale of C*-envelopes. We conjecture that these C*-envelopes are all *-isomorphic and verify this in some important cases.

scholarly journals Ample Spectrum Contractions and Related Fixed Point Theorems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1033 ◽  
Author(s):  
Antonio Francisco Roldán López de Roldán López de Hierro ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Point Of View ◽  
Strict Inequality ◽  
Simple Condition ◽  
Auxiliary Functions ◽  
Simulation Functions ◽  
Contractive Maps ◽  
R Functions

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

scholarly journals Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Mappings ◽  
Random Differential Equations ◽  
Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

scholarly journals On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Cone Metric Spaces ◽  
Fixed Point Properties ◽  
Contractive Maps

We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.

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