Fixed Point Results of Contractive Mappings with Altering Distance Functions in Ordered b-Metric Spaces

2021 ◽  
Vol 10 (2) ◽  
pp. 267-275
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Distance Functions ◽  
Contractive Mappings ◽  
Altering Distance

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.

scholarly journals Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
Shiv Kant Tiwari ◽  
Vishnu Narayan Mishra ◽  
Idrees A. Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Distance Functions ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Partial Metric Spaces

We establish some unique fixed point theorems in complete partial metric spaces for generalized weaklyS-contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results.

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.

scholarly journals Some interesting results on F-metric spaces

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3257-3268 ◽  
Author(s):  
Ashis Beraz ◽  
Hiranmoy Garai ◽  
Bosko Damjanovic ◽  
Ankush Chanda
Keyword(s):  
Fixed Point ◽  
Open Problem ◽  
Metric Spaces ◽  
Distance Functions ◽  
Contractive Mappings ◽  
Open Set ◽  
Altering Distance ◽  
Contractive Type ◽  
Countability Axiom

In this manuscript, we prove that the newly introduced F-metric spaces are Hausdorff and first countable. We investigate some interrelations among the Lindel?fness, separability and second countability axiom in the setting of F-metric spaces. Moreover, we acquire some interesting fixed point results concerning altering distance functions for contractive type mappings and Kannan type contractive mappings in this exciting context. In addition, most of the findings are well-furnished by several non-trivial examples. Finally, we raise an open problem regarding the structure of an open set in this setting.

scholarly journals Generalized Altering Distances and Common Fixed Points in Ordered Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Hassen Aydi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Common Fixed Points ◽  
Distance Functions ◽  
Ordered Metric Spaces ◽  
System Of Integral Equations ◽  
Common Solution ◽  
Altering Distance

Coincidence point and common fixed point results with the concept of generalized altering distance functions in complete ordered metric spaces are derived. These results generalize the existing fixed point results in the literature. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. As an application, we study the existence of a common solution to a system of integral equations.

scholarly journals Fixed Point Theorems for a Class ofα-Admissible Contractions and Applications to Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Selma Gülyaz ◽  
Erdal Karapınar ◽  
İncı M. Erhan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Distance Functions ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Altering Distance

A class ofα-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

scholarly journals Discussion on Generalized-(αψ,βφ)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Maher Berzig ◽  
Erdal Karapınar ◽  
Antonio-Francisco Roldán-López-de-Hierro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Contractive Mapping ◽  
Binary Relations ◽  
Contractive Mappings ◽  
Altering Distance ◽  
Wide Range ◽  
Generalized Altering Distance Function

We extend the notion of (αψ,βφ)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.

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