Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions
In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.)...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-04-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/5/971 |
| _version_ | 1797598253019037696 |
|---|---|
| author | Nihal Taş Elif Kaplan Dania Santina Nabil Mlaiki Wasfi Shatanawi |
| author_facet | Nihal Taş Elif Kaplan Dania Santina Nabil Mlaiki Wasfi Shatanawi |
| author_sort | Nihal Taş |
| collection | DOAJ |
| description | In this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.) on both metric spaces (M-s) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">S</mi></semantics></math></inline-formula>-(M-s) where the symmetry condition is satisfied, and we utilize them to establish a common (F.C.). We prove new (F.C.) results on both (M-s) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">S</mi></semantics></math></inline-formula>-(M-s) with illustrative examples. Finally, we provide an application to activation functions such as rectified linear unit activation functions and parametric rectified linear unit activation functions. |
| first_indexed | 2024-03-11T03:16:43Z |
| format | Article |
| id | doaj.art-c3a9560288654062a7793747c66f3d6a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:43Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-c3a9560288654062a7793747c66f3d6a2023-11-18T03:29:02ZengMDPI AGSymmetry2073-89942023-04-0115597110.3390/sym15050971Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation FunctionsNihal Taş0Elif Kaplan1Dania Santina2Nabil Mlaiki3Wasfi Shatanawi4Department of Mathematics, Balıkesir University, 10145 Balıkesir, TürkiyeDepartment of Mathematics, Ondokuz Mayıs University, 55200 Samsun, TürkiyeDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaIn this paper, we modify various contractive conditions (C.C.)s such as Ciric type (C.C.), Rhoades type (C.C.), Seghal type (C.C.), Bianchini type (C.C.), and Berinde type (C.C.) for two self-mappings, considering that the contractive property plays a major role in establishing a fixed circle (F.C.) on both metric spaces (M-s) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">S</mi></semantics></math></inline-formula>-(M-s) where the symmetry condition is satisfied, and we utilize them to establish a common (F.C.). We prove new (F.C.) results on both (M-s) and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">S</mi></semantics></math></inline-formula>-(M-s) with illustrative examples. Finally, we provide an application to activation functions such as rectified linear unit activation functions and parametric rectified linear unit activation functions.https://www.mdpi.com/2073-8994/15/5/971common fixed circlefixed point𝕊-metric spacesactivation functions |
| spellingShingle | Nihal Taş Elif Kaplan Dania Santina Nabil Mlaiki Wasfi Shatanawi Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions Symmetry common fixed circle fixed point 𝕊-metric spaces activation functions |
| title | Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions |
| title_full | Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions |
| title_fullStr | Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions |
| title_full_unstemmed | Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions |
| title_short | Some Common Fixed Circle Results on Metric and 𝕊-Metric Spaces with an Application to Activation Functions |
| title_sort | some common fixed circle results on metric and 𝕊 metric spaces with an application to activation functions |
| topic | common fixed circle fixed point 𝕊-metric spaces activation functions |
| url | https://www.mdpi.com/2073-8994/15/5/971 |
| work_keys_str_mv | AT nihaltas somecommonfixedcircleresultsonmetricandsmetricspaceswithanapplicationtoactivationfunctions AT elifkaplan somecommonfixedcircleresultsonmetricandsmetricspaceswithanapplicationtoactivationfunctions AT daniasantina somecommonfixedcircleresultsonmetricandsmetricspaceswithanapplicationtoactivationfunctions AT nabilmlaiki somecommonfixedcircleresultsonmetricandsmetricspaceswithanapplicationtoactivationfunctions AT wasfishatanawi somecommonfixedcircleresultsonmetricandsmetricspaceswithanapplicationtoactivationfunctions |