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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: P(s, r) <= P(s, z) + eta (z, r)P(z, r), and keeping the symmetry condition that is P(s, r) = P(r, s) for all r, s....

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Main Authors: Santina, Dania, Othman, Wan Ainun Mior, Wong, Kok Bin, Mlaiki, Nabil
Format: Article
Published: MDPI 2023
Subjects:
Q Science (General)
QA Mathematics
Online Access:http://eprints.um.edu.my/38734/
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spelling my.um.eprints.387342024-11-04T04:30:03Z http://eprints.um.edu.my/38734/ New generalization of metric-type spaces-strong controlled Santina, Dania Othman, Wan Ainun Mior Wong, Kok Bin Mlaiki, Nabil Q Science (General) QA Mathematics 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: P(s, r) <= P(s, z) + eta (z, r)P(z, r), and keeping the symmetry condition that is P(s, r) = P(r, s) for all r, 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. MDPI 2023-02 Article PeerReviewed Santina, Dania and Othman, Wan Ainun Mior and Wong, Kok Bin and Mlaiki, Nabil (2023) New generalization of metric-type spaces-strong controlled. Symmetry-Basel, 15 (2). ISSN 2073-8994, DOI https://doi.org/10.3390/sym15020416 <https://doi.org/10.3390/sym15020416>. 10.3390/sym15020416
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic Q Science (General)
QA Mathematics
spellingShingle Q Science (General)
QA Mathematics
Santina, Dania
Othman, Wan Ainun Mior
Wong, Kok Bin
Mlaiki, Nabil
New generalization of metric-type spaces-strong controlled
description 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: P(s, r) <= P(s, z) + eta (z, r)P(z, r), and keeping the symmetry condition that is P(s, r) = P(r, s) for all r, 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.
format Article
author Santina, Dania
Othman, Wan Ainun Mior
Wong, Kok Bin
Mlaiki, Nabil
author_facet Santina, Dania
Othman, Wan Ainun Mior
Wong, Kok Bin
Mlaiki, Nabil
author_sort Santina, Dania
title New generalization of metric-type spaces-strong controlled
title_short New generalization of metric-type spaces-strong controlled
title_full New generalization of metric-type spaces-strong controlled
title_fullStr New generalization of metric-type spaces-strong controlled
title_full_unstemmed New generalization of metric-type spaces-strong controlled
title_sort new generalization of metric-type spaces-strong controlled
publisher MDPI
publishDate 2023
url http://eprints.um.edu.my/38734/
_version_ 1814933221289230336
score 13.211869

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