scholarly journals Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

2021 ◽  
pp. 3031-3038
Author(s):  
Raghad I. Sabri
Keyword(s):  
Functional Analysis ◽  
Continuous Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Compactness Property ◽  
Locally Compact ◽  
Fuzzy Metric Spaces ◽  
Fundamental Properties ◽  
Definition Of

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.    Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studied and some essential theorems are proved.

scholarly journals The Continuity of Fuzzy Metric Spaces

2021 ◽  
Vol 7 (4) ◽  
pp. 85
Author(s):  
Mohammed S. Rasheed
Keyword(s):  
Continuous Function ◽  
Open Subset ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

<p>In the present paper, the definitions of a fuzzy continuous function and uniformly fuzzy continuous  are introduced. we prove that a function  from a fuzzy metric space ( ) into a fuzzy metric space ( )  is fuzzy continuous if and only if for every fuzzy open subset  of ,   is fuzzy open in . Also the composition function of two uniformly fuzzy continuous functions is proved to be a uniformly fuzzy continuous function.</p>

scholarly journals THE PROPERTIES OF OCCASIONALLY WEAKLY COMPATIBLE MAPPING ON FUZZY METRIC SPACES

EDUPEDIA ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 33
Author(s):  
Citra Rizki ◽  
Sumaji .
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weakly Compatible ◽  
Compatible Mapping ◽  
Definition Of

In this paper, describe about the properties of occasionally weakly compatible mapping on fuzzy metric spaces in terms of fixed point theory. The discussion of this research is strarted from the concept of fuzzy set and metric space and they were expanded into the concept of fuzzy metric space using continuous norm-t. Furthermore, in investigating about occasionally weakly compatible mapping on fuzzy metric space, we start by given the definition of compatible mapping, weakly commuting, and weakly compatible. Moreover, we construct some theorems to investigating the properties of occasionally weakly compatible mapping on fuzzy metric spaces. 

scholarly journals U(X) as a ring for metric spaces X

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1981-1984 ◽  
Author(s):  
Sànchez Cabello
Keyword(s):  
Continuous Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Infinite Subset ◽  
Short Paper ◽  
Uniformly Continuous Function ◽  
Uniformly Continuous

In this short paper, we will show that the space of real valued uniformly continuous functions defined on a metric space (X,d) is a ring if and only if every subset A ? X has one of the following properties: ? A is Bourbaki-bounded, i.e., every uniformly continuous function on X is bounded on A. ? A contains an infinite uniformly isolated subset, i.e., there exist ? > 0 and an infinite subset F ? A such that d(a,x) ? ? for every a ? F, x ? X n \{a}.

scholarly journals More about metric spaces on which continuous functions are uniformly continuous

1986 ◽  
Vol 33 (3) ◽  
pp. 397-406 ◽  
Author(s):  
Gerald Beer
Keyword(s):  
Fixed Point ◽  
Continuous Function ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Function Form ◽  
Uniformly Continuous

An Atsuji space is a metric space X such that each continuous function form X to an arbitrary metric space Y is uniformly continuous. We here present (i) characterizations of metric spaces with Atsuji completions; (ii) Cantor-type theorems for Atsuji spaces; (iii) a fixed point theorem for self-maps of an Atsuji space.

scholarly journals A Meir-Keeler type fixed point theorem in fuzzy metric spaces

2016 ◽  
Vol 12 (11) ◽  
pp. 6778-6784 ◽  
Author(s):  
Siditë Duraj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Definition Of

In this paper we introduce a new definition of Meir-Keeler type contractions and prove a fixed point theorem for them in fuzzy metric space.

scholarly journals Fixed Point of Interpolative Rus–Reich–Ćirić Contraction Mapping on Rectangular Quasi-Partial b-Metric Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 32
Author(s):  
Pragati Gautam ◽  
Luis Manuel Sánchez Ruiz ◽  
Swapnil Verma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Real Number ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Rectangular Metric Space ◽  
New Type ◽  
Symmetry Requirement ◽  
Definition Of

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

scholarly journals Strong submeasures and applications to non-compact dynamical systems

2020 ◽  
pp. 1-23
Author(s):  
TUYEN TRUNG TRUONG
Keyword(s):  
Metric Space ◽  
Bounded Operator ◽  
Continuous Functions ◽  
Open Dense Subset ◽  
Compact Metric Space ◽  
Basic Properties ◽  
Banach Theorem ◽  
Complex Varieties ◽  
Definition Of ◽  
Meromorphic Maps

Abstract A strong submeasure on a compact metric space X is a sub-linear and bounded operator on the space of continuous functions on X. A strong submeasure is positive if it is non-decreasing. By the Hahn–Banach theorem, a positive strong submeasure is the supremum of a non-empty collection of measures whose masses are uniformly bounded from above. There are many natural examples of continuous maps of the form $f:U\rightarrow X$ , where X is a compact metric space and $U\subset X$ is an open-dense subset, where f cannot extend to a reasonable function on X. We can mention cases such as transcendental maps of $\mathbb {C}$ , meromorphic maps on compact complex varieties, or continuous self-maps $f:U\rightarrow U$ of a dense open subset $U\subset X$ where X is a compact metric space. For the aforementioned mentioned the use of measures is not sufficient to establish the basic properties of ergodic theory, such as the existence of invariant measures or a reasonable definition of measure-theoretic entropy and topological entropy. In this paper we show that strong submeasures can be used to completely resolve the issue and establish these basic properties. In another paper we apply strong submeasures to the intersection of positive closed $(1,1)$ currents on compact Kähler manifolds.

scholarly journals Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 884 ◽  
Author(s):  
Tahair Rasham ◽  
Giuseppe Marino ◽  
Abdullah Shoaib
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Contractive Condition ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Dislocated Metric Space ◽  
Definition Of ◽  
Dislocated Metric

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

scholarly journals Approximations of Variational Problems in Terms of Variational Convergence

2017 ◽  
Vol 20 (K2) ◽  
pp. 107-116
Author(s):  
Diem Thi Hong Huynh
Keyword(s):  
Multiobjective Optimization ◽  
Metric Space ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Variational Problems ◽  
Dimensional Case ◽  
Variational Convergence ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Definition Of

We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

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