New Generalization of Metric-Type Spaces—Strong Controlled

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: ℘(s,r)≤℘(s,z)+η(z,r)℘(z,r), and keeping the symmetry condition that is ℘(s,r)=℘(r,s)forallr,s. We demonstrate the exi...

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Bibliographic Details
Published in:Symmetry (Basel) 2023-02, Vol.15 (2), p.416
Main Authors: Santina, Dania, Mior Othman, Wan Ainun, Wong, Kok Bin, Mlaiki, Nabil
Format: Article
Language:English
Subjects:
a double-controlled metric type
Differential equations
fixed-point and strong controlled metric-type space (SCMTS)
Fractional calculus
Inequality
Linear equations
Mathematical analysis
Metric space
Polynomials
strong b−metric space (SbMS)
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Summary:In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: ℘(s,r)≤℘(s,z)+η(z,r)℘(z,r), and keeping the symmetry condition that is ℘(s,r)=℘(r,s)forallr,s. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15020416