scholarly journals New fixed point results for contractive maps involving dominating auxiliary functions

2016 ◽  
Vol 09 (06) ◽  
pp. 4114-4126 ◽  
Author(s):  
Nawab Hussain ◽  
Abdul Latif ◽  
Peyman Salimi
Keyword(s):  
Fixed Point ◽  
Auxiliary Functions ◽  
Contractive Maps

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 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 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.

scholarly journals Suzuki-Edelstein Type Contractions via Auxiliary Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Peyman Salimi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Complete Metric Space ◽  
Existence Results ◽  
Partially Ordered ◽  
Auxiliary Functions ◽  
Type Mapping

We prove the existence and uniqueness of a fixed point of certain type mapping, extension of Suzuki-Edelstein mapping, in a partially ordered complete metric space. Our results extend, improve, and generalize the existence results on the topic in the literature. We state some examples to illustrate our results.

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