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 Some Generalized Contraction Classes and Common Fixed Points in b-Metric Space Endowed with a Graph

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 754 ◽  
Author(s):  
Reny George ◽  
Hossam A Nabwey ◽  
Rajagopalan Ramaswamy ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Pair ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Generalized Contraction ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

We have introduced the new notions of R-weakly graph preserving and R-weakly α -admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as α -admissible mappings of type S, α * -admissible mappings of type S and α * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly α -admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

scholarly journals Common Fixed Point Theorems for Nonlinear Contractive Mappings in Dislocated Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yijie Ren ◽  
Junlei Li ◽  
Yanrong Yu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Mapping Theorem ◽  
Contractive Mappings ◽  
Dislocated Metric Space ◽  
Common Fixed Point Theorems ◽  
Dislocated Metric

In 1986, Matthews generalized Banach contraction mapping theorem in dislocated metric space that is a wider space than metric space. In this paper, we established common fixed point theorems for a class of contractive mappings. Our results extend the corresponding ones of other authors in dislocated metric spaces.

scholarly journals Generalized Contractive Mappings and Weaklyα-Admissible Pairs inG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
N. Hussain ◽  
V. Parvaneh ◽  
S. J. Hoseini Ghoncheh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Periodic Points ◽  
Contractive Mappings ◽  
Admissible Pairs ◽  
Weakly Contractive ◽  
Common Fixed Point Theorems

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ,φ)-contractive mappings using partially weaklyG-α-admissibility in the setup ofG-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially orderedG-metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.

scholarly journals Maia type fixed point results via C-class function

2020 ◽  
Vol 12 (2) ◽  
pp. 227-244
Author(s):  
Arslan Hojat Ansari ◽  
Mohammad Saeed Khan ◽  
Vladimir Rakočević
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Binary Relation ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Class Function ◽  
Banach’S Fixed Point Theorem

AbstractIn 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.

scholarly journals Common fixed point theorems of contractive-type mappings

2004 ◽  
Vol 2004 (53) ◽  
pp. 2809-2819
Author(s):  
Hee Soo Park ◽  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contractive Mappings ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Using the concept ofD-metric we prove some common fixed point theorems for generalized contractive mappings on a completeD-metric space. Our results extend, improve, and unify results of Fisher and Ćirić.

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 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 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.

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.

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