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 points under strict conditions

2020 ◽  
Vol 24 (2) ◽  
pp. 63-70
Author(s):  
Hakima Bouhadjera ◽  
Said Beloul ◽  
Achref Tabet
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
New Concepts ◽  
Common Fixed Point Theorems

In this contribution, three new concepts called reciprocally continuous, strictly subweakly compatible and strictly subreciprocally continuous single and multivalued mappings are given for obtention some common fixed point theorems in a metric space. Our results improve and complement the results of Aliouche and Popa, Azam and Beg, Deshpande and Pathak, Kaneko and Sessa, Popa and others.

scholarly journals Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jamshaid Ahmad ◽  
Chakkrid Klin-Eam ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Complex Valued Metric Space ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

scholarly journals Complex Valued b-Metric Spaces and Common Fixed Point Theorems under Rational Contractions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Anil Kumar Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued b-metric space. The obtained results generalize and extend some of the well-known results in the literature.

scholarly journals On common fixed points of pairs of a single and a multivalued coincidentally commuting mappings inD-metric spaces

2003 ◽  
Vol 2003 (40) ◽  
pp. 2519-2539
Author(s):  
B. C. Dhage ◽  
A. Jennifer Asha ◽  
S. M. Kang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Generalized Contraction ◽  
Contraction Condition ◽  
Common Fixed Point Theorems ◽  
Commuting Mappings

The present paper studies some common fixed-point theorems for pairs of a single-valued and a multivalued coincidentally commuting mappings inD-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems inD-metric spaces including those of Dhage (2000) and Rhoades (1996).

On common fixed points for a family of mappings

1975 ◽  
Vol 13 (2) ◽  
pp. 261-267 ◽  
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems

The purpose of this paper is to obtain some common fixed point theorems for a family of mappings in a complete metric space. The results herein improve some of the recent theorems of Kiyoshi Iséki (Bull. Austral. Math. Soc. 10 (1974), 365–370).

scholarly journals Common fixed point theorems for several multivalued mappings on proximinal sets in regular modular space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
N. Faried ◽  
H. Abd El-Ghaffar ◽  
S. Hamdy
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Modular Space ◽  
Multivalued Mappings ◽  
Modular Metric Space ◽  
Proximinal Sets ◽  
Common Fixed Point Theorems

AbstractIn this paper, we found a common fixed point for several multivalued mappings on proximinal sets in regular modular metric space. Also, we introduced the notions of conjoint F-proximinal contraction as well as conjoint F-proximinal contraction of Hardy–Rogers-type for several multivalued mappings. Furthermore, we enhanced our results by giving an application in integral equations.

scholarly journals Solving Integral Equations by Common Fixed Point Theorems on Complex Partial b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Arul Joseph Gnanaprakasam ◽  
Salah Mahmoud Boulaaras ◽  
Gunaseelan Mani ◽  
Mohamed Abdalla ◽  
Asma Alharbi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

In this paper, we prove some common fixed point theorems for rational contraction mapping on complex partial b -metric space. The presented results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

scholarly journals Common Fixed Points of Compatible Mappings

2012 ◽  
Vol 4 (3) ◽  
pp. 603-608
Author(s):  
M. P. Singh ◽  
R. Yumnam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Common Fixed Points ◽  
Compatible Mappings ◽  
Type B ◽  
Common Fixed Point Theorems

In this paper we prove two common fixed point theorems by considering four mappings in complete metric space. In the first theorem we consider two pairs of compatible mappings of type (A) and in the second theorem we consider two pairs of compatible mappings of type (B). Our results modify and extend some earlier results in the literature.© 2012 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v4i3.10567 J. Sci. Res. 4 (3), 603-608 (2012)

Some Fixed and Common Fixed Point Theorems in Metric Spaces

1974 ◽  
Vol 17 (2) ◽  
pp. 257-259 ◽  
Author(s):  
V. M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Image Position ◽  
Common Fixed Point Theorems

Let (X, d) be a metric space and Ti(i=l, 2) be self mappings of X. The purpose of this paper is to investigate the fixed and common fixed points of Ti, when the pair Ti(i=l, 2) satisfies a condition of the following type:(1)

scholarly journals On common fixed points in generalized Menger spaces

2016 ◽  
Vol 5 (4) ◽  
pp. 197
Author(s):  
Salwa Abed ◽  
Hadeel Hussein Luaibi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Suitable Condition ◽  
Common Fixed Points ◽  
Menger Space ◽  
Iteration Sequence ◽  
Menger Spaces ◽  
Common Fixed Point Theorems

R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

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