scholarly journals A different approach to b(an,bn)-hypermetric spaces

2022 ◽  
Vol 70 (1) ◽  
pp. 24-42
Author(s):  
Nezhad Deghan ◽  
Nikola Mirkov ◽  
Vesna Todorčević ◽  
Stojan Radenović
Keyword(s):  
Functional Analysis ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Positive Definiteness ◽  
Theoretical Methods ◽  
The Fixed Point Theorem ◽  
Initial Results

Introduction/purpose: The aim of this paper is to present the concept of b(an,bn)-hypermetric spaces. Methods: Conventional theoretical methods of functional analysis. Results: This study presents the initial results on the topic of b(an,bn)-hypermetric spaces. In the first part, we generalize an n-dimensional (n ≥ 2) hypermetric distance over an arbitrary non-empty set X. The b(an,bn)-hyperdistance function is defined in any way we like, the only constraint being the simultaneous satisfaction of the three properties, viz, non-negativity and positive-definiteness, symmetry and (an, bn)-triangle inequality. In the second part, we discuss the concept of (an, bn)-completeness, with respect to this b(an,bn)-hypermetric, and the fixed point theorem which plays an important role in applied mathematics in a variety of fields. Conclusion: With proper generalisations, it is possible to formulate well-known results of classical metric spaces to the case of b(an,bn)-hypermetric spaces.

scholarly journals A new version of the results of UN-hypermetric spaces

2021 ◽  
Vol 69 (3) ◽  
pp. 562-577
Author(s):  
Nezhad Dehghan ◽  
Ahmadreza Forough ◽  
Nikola Mirkov ◽  
Stojan Radenović
Keyword(s):  
Functional Analysis ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Applied Mathematics ◽  
Distance Measures ◽  
Theoretical Methods ◽  
Universal Properties ◽  
The Fixed Point Theorem

Introduction/purpose: The aim of this paper is to present the concept of a universal hypermetric space. An n-dimensional (n ≥ 2) hypermetric distance over an arbitrary non-empty set X is generalized. This hypermetric distance measures how separated all n points of the space are. The paper discusses the concept of completeness, with respect to this hypermetric as well as the fixed point theorem which play an important role in applied mathematics in a variety of fields. Methods: Standard proof based theoretical methods of the functional analysis are employed. Results: The concept of a universal hypermetric space is presented. The universal properties of hypermetric spaces are described. Conclusion: This new version of the results for UN-hypermetric spaces may have applications in various disciplines where the degree of clustering is sought for.

scholarly journals On statistical convergence in quasi-metric spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 225-236 ◽  
Author(s):  
Merve İlkhan ◽  
Emrah Evren Kara
Keyword(s):  
Functional Analysis ◽  
Computer Science ◽  
Distance Function ◽  
Metric Space ◽  
Statistical Convergence ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Comprehensive Investigation ◽  
Cauchy Sequences

AbstractA quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric in general. Quasi-metrics are a subject of comprehensive investigation both in pure and applied mathematics in areas such as in functional analysis, topology and computer science. The main purpose of this paper is to extend the convergence and Cauchy conditions in a quasi-metric space by using the notion of asymptotic density. Furthermore, some results obtained are related to completeness, compactness and precompactness in this setting using statistically Cauchy sequences.

scholarly journals Fixed point theorem for compatible mappings in intuitionistic fuzzy 3-metric spaces

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 371-376
Author(s):  
Hassan Abu-Donia ◽  
Hany Atia ◽  
Omnia Khater
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Main Idea ◽  
Intuitionistic Fuzzy ◽  
Uniqueness And Existence ◽  
The Fixed Point Theorem ◽  
Asymptotically Regular

In this paper, we introduced the concept of weak compatible of type (?) and asymptotically regular defined on intuitionistic fuzzy 3-metric space and proved the uniqueness and existence the fixed point theorem for five mappings from a complete intuitionistic fuzzy 3-metric space into itself under weak compatible of type (?) and asymptotically regular. The used definitions and theorem show the practice of our main idea.

scholarly journals A fixed point theorem in generalized metric spaces

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Luljeta Kikina ◽  
Kristaq Kikina
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric

AbstractA generalized metric space has been defined by Branciari as a metric space in which the triangle inequality is replaced by a more general inequality. Subsequently, some classical metric fixed point theorems have been transferred to such a space. In this paper, we continue in this direction and prove a version of Fisher’s fixed point theorem in generalized metric spaces.

scholarly journals Fixed-Point Theorem for Multivalued Quasi-Contraction Maps in a V-Fuzzy Metric Space

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Matthew Brijesh Sookoo ◽  
Sreedhara Rao Gunakala
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric ◽  
The Fixed Point Theorem ◽  
Contraction Maps

In this paper, we introduce the concept of a set-valued or multivalued quasi-contraction mapping in V-fuzzy metric spaces. Using this new concept, a fixed-point theorem is established. We also provide an example verifying and illustrating the fixed-point theorem in action.

scholarly journals Some Common Fixed Point Theorems in Partial Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Erdal Karapınar ◽  
Uğur Yüksel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Triangle Inequality ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Partial Metric Space ◽  
Partial Metric ◽  
Partial Metric Spaces ◽  
Common Fixed Point Theorems

Many problems in pure and applied mathematics reduce to a problem of common fixed point of some self-mapping operators which are defined on metric spaces. One of the generalizations of metric spaces is the partial metric space in which self-distance of points need not to be zero but the property of symmetric and modified version of triangle inequality is satisfied. In this paper, some well-known results on common fixed point are investigated and generalized to the class of partial metric spaces.

scholarly journals Existence and approximation of fixed points in convex metric spaces

2014 ◽  
Vol 30 (2) ◽  
pp. 175-185
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Generalized Nonexpansive Mapping ◽  
The Fixed Point Theorem

A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.

scholarly journals Fixed point theorem for compatible mappings in intuitionistic fuzzy 3-metric spaces

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 371-376
Author(s):  
Hassan Abu-Donia ◽  
Hany Atia ◽  
Omnia Khater
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Main Idea ◽  
Intuitionistic Fuzzy ◽  
Uniqueness And Existence ◽  
The Fixed Point Theorem ◽  
Asymptotically Regular

In this paper, we introduced the concept of weak compatible of type (?) and asymptotically regular defined on intuitionistic fuzzy 3-metric space and proved the uniqueness and existence the fixed point theorem for five mappings from a complete intuitionistic fuzzy 3-metric space into itself under weak compatible of type (?) and asymptotically regular. The used definitions and theorem show the practice of our main idea.

scholarly journals Convex Fuzzy Soft Metric Space

2020 ◽  
Vol 7 (3) ◽  
pp. 78-82
Author(s):  
M Vasuky ◽  
A Uma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Convex Structure ◽  
The Fixed Point Theorem

In this paper, we investigate the concept of fuzzy soft metric space in terms of fuzzy soft points. The convex structure of fuzzy soft metric spaces is defined and we introduce the convex fuzzy soft metric space. Also we established the fixed point theorem of convex fuzzy soft metric space.

scholarly journals A NOTE ON THE PAPER “ON COMPLETENESS IN METRIC SPACES AND FIXED POINT THEOREMS"

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Deepak Khantwal ◽  
Umesh Cuandra Gairola
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Continuous Mappings ◽  
Discontinuous Mappings ◽  
The Fixed Point Theorem ◽  
Common Fixed Point Theorem

In the present note, we show that the assumption of continuity used in the fixed point theorem of Gregori et al. (Results Math. 73 (2018), no. 4, Art. 142, 13) can be relaxed to some weaker version of continuity. More precisely, we prove a fixed point theorem for orbitally continuous and k-continuous mappings in weak G-complete metric space and provide an appropriate example to show that our result is not only valid for continuous mappings but also for some discontinuous mappings. Moreover, we apply our main result to establish a common fixed point theorem for two self-mappings

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