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.

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 Common fixed point theorems for generalized G- η-χ–contractive type mappings with applications

2017 ◽  
Vol 37 (1) ◽  
pp. 9-20
Author(s):  
Manoj Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of alpha-psi-contractive type mappings in metric spaces. In 2013, Alghamdi et. al. [2] introduced the concept of G-β--contractive type mappings in G-metric spaces. Our aim is to introduce new concept of generalized G-η-χ-contractive pair of mappings. Further, we study some fixed point theorems for such mappings in complete G-metric spaces. As an application, we further establish common fixed point theorems for G-metric spaces for cyclic contractive mappings.

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 On contractive mappings and discontinuity at fixed points

2020 ◽  
Vol 14 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Hiranmoy Garai ◽  
Lakshmi Dey ◽  
Yeol Cho
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Open Problem ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Compact Metric Spaces ◽  
Contractive Mappings ◽  
Interesting Open Problem

This paper deals with an interesting open problem of B.E. Rhoades (Contemporary Math. (Amer. Math. Soc.) 72(1988), 233-245) on the existence of general contractive conditions which have fixed points, but are not necessarily continuous at the fixed points. We propose some more solutions to this problem by introducing two new types of contractive mappings, that is, A-contractive and A`-contractive, which are, in some sense, more appropriate than those of the important previous attempts. We establish some new fixed point results involving these two contractive mappings in compact metric spaces and also in complete metric spaces and show that these contractive mappings are not necessarily continuous at their fixed points. Finally, we suggest an applicable area, where our main results may be employed.

scholarly journals Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
New Class ◽  
Contractive Mappings ◽  
Contractive Type

We establish fixed point theorems for a new class of contractive mappings. As consequences of our main results, we obtain fixed point theorems on metric spaces endowed with a partial order and fixed point theorems for cyclic contractive mappings. Various examples are presented to illustrate our obtained results.

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