scholarly journals Coincidence and common fixed point results under generalized (A,S)f-contractions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2651-2666 ◽  
Author(s):  
Waleed Alfaqih ◽  
Rqeeb Gubran ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space

Very recently, Shahzad et al. [RACSAM 111 (2017) 307-324] introduced the notion of (A,S)- contractions which unifies several well known nonlinear type contractions (e.g. R-contractions, Z-contractions, L-contractions etc.) in one go. In this paper, we introduce the notion of generalized (A,S)f-contractions and utilize the same to present some coincidence and common fixed point results for a pair of self-mappings (g,f)defined on a metric space endowed with a binary relation S. In this course, we ought to introduce some new notions namely: (I,S)-continuity, (I,S)-compatibility and local (g,f)-transitivity. Consequently, several results involving R-contractions and Z-contractions are deduced. Finally, we furnish illustrative examples to demonstrate the utility of our results.

scholarly journals Employing Locally Finitely T-Transitive Binary Relations to Prove Coincidence Theorems for Nonlinear Contractions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mohammad Arif ◽  
Idrees A. Khan ◽  
Mohammad Imdad ◽  
Aftab Alam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Binary Relations ◽  
Nonlinear Contraction ◽  
Coincidence Theorems ◽  
Nonlinear Contractions ◽  
Transitive Binary Relation

In this article, we prove some relation-theoretic results on coincidence and common fixed point for a nonlinear contraction employing a locally finitely T-transitive binary relation, where T stands for a self-mapping on the underlying metric space. Our newly proved results deduce sharpened versions of certain relevant results of the existing literature. Finally, we adopt some examples to substantiate the genuineness of our proved results herein.

scholarly journals On interpolative F-contractions with shrink map

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Muhammad Usman Ali
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Result

AbstractIn this article, we introduce two notions of interpolative F-contractions with shrink map and F-contractions with shrink map. We also study the existence of E-fixed points by using these notations on a metric space endowed with a binary relation. As an application and consequence of the main results, we also get some other interesting results like a common fixed point result, an E-fixed point result on a metric space equipped with graph, and an existence theorem for a solution of integral equations.

scholarly journals Fixed point results for weakly α-admissible pairs

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3697-3713 ◽  
Author(s):  
Ljubomir Ciric ◽  
Vahid Parvaneh ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Pair ◽  
Contractive Mappings ◽  
Admissible Pairs

In this paper, we introduce the concepts of weakly and partially weakly ?-admissible pair of mappings and obtain certain coincidence and fixed point theorems for classes of weakly ?-admissible contractive mappings in a b-metric space. As an application, we derive some new coincidence and common fixed point results in a b-metric space endowed with a binary relation or a graph. Moreover, an example is provided here to illustrate the usability of the obtained results.

scholarly journals Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions

2018 ◽  
Vol 19 (1) ◽  
pp. 65
Author(s):  
Md Ahmadullah ◽  
Mohammad Imdad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems ◽  
Nonlinear Contractions

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))]  and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

scholarly journals Extraction new results of common fixed point theorems for $({T}, {\alpha }_{{s}}, {F})$-contraction of six mappings in a tripled b-metric space with an application of integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Mohammad Esmael Samei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Solution ◽  
Type Integral ◽  
First Time ◽  
Common Fixed Point Theorems

Abstract The aim of this work is to usher in tripled b-metric spaces, triple weakly $\alpha _{s}$ α s -admissible, triangular partially triple weakly $\alpha _{s}$ α s -admissible and their properties for the first time. Also, we prove some theorems about coincidence and common fixed point for six self-mappings. On the other hand, we present a new model, talk over an application of our results to establish the existence of common solution of the system of Volterra-type integral equations in a triple b-metric space. Also, we give some example to illustrate our theorems in the section of main results. Finally, we show an application of primary results.

scholarly journals On Complete Cone Metric Space and Fixed Point Theorem

2011 ◽  
Vol 3 (2) ◽  
pp. 303-309
Author(s):  
J. Mehta ◽  
M. L. Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weakly Compatible Maps ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Contractive Type ◽  
Cone Metric

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.Keywords: Common fixed point; Complete cone metric space; Weakly compatible maps.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6475                J. Sci. Res. 3 (2), 303-309 (2011)

Coupled coincidence and coupled common fixed point theorems on a fuzzy metric space with a graph

2018 ◽  
Vol 34 (3) ◽  
pp. 417-424
Author(s):  
PHUMIN SUMALAI ◽  
◽  
POOM KUMAM ◽  
DHANANJAY GOPAL ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric ◽  
Coupled Common Fixed Point ◽  
Common Fixed Point Theorems ◽  
Coupled Coincidence

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1–14], we introduce a new class of G − f−contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

scholarly journals A common fixed point theorem of Meir and Keeler type

1993 ◽  
Vol 16 (4) ◽  
pp. 669-674 ◽  
Author(s):  
Y. J. Cho ◽  
P. P. Murthy ◽  
G. Jungck
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Compatible Mappings ◽  
Common Fixed Point Theorem

In this paper, we introduce the concept of compatible mappings of type (A) on a metric space, which is equivalent to the concept of compatible mappings under some conditions, and give a common fixed point theorem of Meir and Keeler type. Our result extends, generalized and improves some results of Meir-Keeler, Park-Bae, Park-Rhoades, Pant and Rao-Rao, etc.

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