A GENERALIZATION OF AN EXTENDED b-METRIC SPACE AND SOME FIXED POINT THEOREMS

2021 ◽  
Vol 10 (5) ◽  
pp. 2351-2360
Author(s):  
V. Singh ◽  
P. Singh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Lipschitz Constant ◽  
Contraction Mappings ◽  
Underlying Space ◽  
Comparison Functions

In this paper, we present fixed point theorems for contraction mappings in a generalization of an extended $b$-metric space where the product of the Lipschitz constant and functions of the underlying space in the limit are bounded by one for sequences in an orbit. Futhermore, we prove fixed point results in which the contraction involves $b$-comparison functions.

FIXED POINT THEOREMS IN A WEIGHTED RECTANGULAR b-METRIC SPACE

2021 ◽  
Vol 10 (4) ◽  
pp. 2157-2165
Author(s):  
P. Singh ◽  
V. Singh
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Lipschitz Constant

In this paper, we provide a generalization of a rectangular b-metric space by relaxing the rectangular inequality to include unequal weights. We provide examples and restrictions for the Lipschitz constant enabling convergence of some sequences in the proof of some fixed point theorems.

Fixed point theorems of contraction mappings in complete b-metric space of zero at infinity varieties

2020 ◽  
Author(s):  
Ghorban Khalilzadeh Ranjbar ◽  
Farhad Hosseinzadeh Lotfi ◽  
Mohammad Esmael Samei ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Contraction Mappings

scholarly journals Some fixed point theorems for set valued directional contraction mappings

1980 ◽  
Vol 3 (3) ◽  
pp. 455-460 ◽  
Author(s):  
V. M. Sehgal
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Contraction Mappings

LetSbe a subset of a metric spaceXand letB(X)be the class of all nonempty bounded subsets ofXwith the Hausdorff pseudometricH. A mappingF:S→B(X)is a directional contraction iff there exists a realα∈[0,1)such that for eachx∈Sandy∈F(x),H(F(x),F(z))≤αd(x,z)for eachz∈[x,y]∩S, where[x,y]={z∈X:d(x,z)+d(z,y)=d(x,y)}. In this paper, sufficient conditions are given under which such mappings have a fixed point.

scholarly journals (C , Ψ * , G ) Class of Contractions and Fixed Points in a Metric Space Endowed with a Graph

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 482 ◽  
Author(s):  
Reny George ◽  
Ekta Tamrakar ◽  
Jelena Vujaković ◽  
Hemant Pathak ◽  
Selvavinayagam Velusamy
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Set ◽  
Contraction Mappings ◽  
Control Functions ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we introduce the ( C , Ψ * , G ) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space.

scholarly journals On Multivalued Fuzzy Contractions in Extended b -Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Nayab Alamgir ◽  
Quanita Kiran ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Contraction Mappings ◽  
Nadler’S Fixed Point Theorem ◽  
The Family ◽  
Fuzzy Fixed Point

In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b -metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α -fuzzy fixed point theorems in the context of extended b -metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α -fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.

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