On a pair of fuzzy dominated mappings on closed ball in the multiplicative metric space with applications

2021 ◽  
Author(s):  
Tahair Rasham ◽  
Muhammad Sajjad Shabbir ◽  
Praveen Agarwal ◽  
Shaher Momani
Keyword(s):  
Metric Space ◽  
Closed Ball ◽  
Multiplicative Metric Space

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

scholarly journals On Unique and Nonunique Fixed Points and Fixed Circles in M v b -Metric Space and Application to Cantilever Beam Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Meena Joshi ◽  
Anita Tomar ◽  
Hossam A. Nabwey ◽  
Reny George
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Metric Space ◽  
Order Differential Equation ◽  
Unique Fixed Point ◽  
Elastic Beam ◽  
Closed Ball ◽  
Open Ball ◽  
Ball Convergence ◽  
Fourth Order Differential Equation

We introduce M v b -metric to generalize and improve M v -metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on M v b -metric space and to create an environment for the survival of a unique fixed point. Also, we introduce a notion of a fixed circle and a fixed disc to study the geometry of the set of nonunique fixed points of a discontinuous self-map and establish fixed circle and fixed disc theorems. Further, we verify all these results by illustrative examples to demonstrate the authenticity of the postulates. Towards the end, we solve a fourth order differential equation arising in the bending of an elastic beam.

scholarly journals In which metric spaces are parallel bodies of closed sets closed?

1983 ◽  
Vol 26 (2) ◽  
pp. 265-273
Author(s):  
Gerald Beer
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Closed Sets ◽  
Parallel Body

Let X be a metric space with metric d and for each x in X let Bλ[x] denote the closed ball of radius λ about x. Following Valentine [15] if K⊂X and λ is positive, then we call the set Bλ[K]=∪x∈KBλ[x] the λ-parallel body of K. The following fact is obvious.

scholarly journals Metric spaces with nice closed balls and distance functions for closed sets

1987 ◽  
Vol 35 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Distance Function ◽  
Metric Space ◽  
Pointwise Convergence ◽  
Metric Spaces ◽  
Closed Ball ◽  
Distance Functions ◽  
Entire Space ◽  
Closed Sets ◽  
Bounded Sets

A metric space 〈X,d〉 is said to have nice closed balls if each closed ball in X is either compact or the entire space. This class of spaces includes the metric spaces in which closed and bounded sets are compact and those for which the distance function is the zero-one metric. We show that these are the spaces in which the relation F = Lim Fn for sequences of closed sets is equivalent to the pointwise convergence of 〈d (.,Fn)〉 to d (.,F). We also reconcile these modes of convergence with three other closely related ones.

scholarly journals Some Fixed Point Theorems in Pseudo Multiplicative Metric Spaces with Convex Structure

2019 ◽  
Author(s):  
Naveed Jamal ◽  
Dr. M. Anwar Chaudhry ◽  
M. Bakhsh Baloch
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Convex Structure ◽  
Multiplicative Metric Spaces ◽  
Multiplicative Metric Space

In the framework of a multiplicative metric space. We have.discuss some Properties of convex.structures.in pseudo multiplicative metric space and have applieditheseiproperties toiobtain alfixed point results in complete pseudo. It would be interesting to prove .some.further results.in such metric.spaces with completeness.property

scholarly journals Fixed Point Results on Multiplicative Semi-Metric Space

2020 ◽  
Vol 12 (3) ◽  
pp. 341-348
Author(s):  
B. Vijayabaskerreddy ◽  
V. Srinivas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Compatible Mappings ◽  
Weakly Compatible ◽  
Continuous Mappings ◽  
Common Fixed Point Theorems ◽  
Multiplicative Metric Space ◽  
Unique Common Fixed Point

  In this paper we introduce the notion of the Multiplicative Semi-Metric Space and proved common fixed point theorems. We establish fixed point theorems for four self-maps which can be extended to derive common fixed point theorems involving any finite number of mappings in Multiplicative Semi Metric Space. Further examples are discussed to show that compatible mappings of type-E, weakly compatible mappings and reciprocally-continuous mappings are weaker forms of compatible mappings and continuous mappings respectively. The main objective of this article is to prove the unique common fixed point theorems and employing the notion of the compatible mappings of type-E, reciprocally-continuous mappings in the Multiplicative Semi Metric Space. Our result generalizes the concept of Multiplicative Metric Space as it does not involve the multiplicative triangle inequality.

scholarly journals Cyclic b -Multiplicative A , B -Hardy–Rogers-Type Local Contraction and Related Results in b -Multiplicative and b -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Abdullah Eqal Al-Mazrooei ◽  
Abdullah Shoaib ◽  
Jamshaid Ahmad
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Closed Set ◽  
Local Contraction ◽  
Multiplicative Metric Space

The aim of this paper is to define cyclic b -multiplicative Hardy–Rogers-type local contraction in the context of generalized spaces named as b -multiplicative spaces to extend various results of the literature including the main results of Yamaod et al. In this way, we apply a new generalized contractive condition only on a closed set instead of a whole set and by using b -multiplicative space instead of multiplicative metric space. We apply our results to obtain new results in b -metric spaces. Examples are given to show the usability of our results, when others cannot.

scholarly journals Fixed Point Results for Multivalued Contractive Mappings Endowed with Graphic Structure

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Tahair Rasham ◽  
Abdullah Shoaib ◽  
Badriah A. S. Alamri ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
Contractive Mappings ◽  
Set Up

The aim of this paper is to introduce the notion of admissible multivalued mappings and to set up fixed point results for such mappings fulfilling generalized locally Ćirić type rational-contractive conditions on a closed ball in complete dislocated b-metric space. Example and application have been given to demonstrate the novelty of our results. Our results combine, extend, and infer several comparable results in the existing literature.

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