Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming
The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed linear spaces as they are defined by Nădăban and...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-09-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/14/10/1966 |
| _version_ | 1797469864548368384 |
|---|---|
| author | Tudor Bînzar Flavius Pater Sorin Nădăban |
| author_facet | Tudor Bînzar Flavius Pater Sorin Nădăban |
| author_sort | Tudor Bînzar |
| collection | DOAJ |
| description | The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed linear spaces as they are defined by Nădăban and Dzitac. When completeness is required, we will use the George and Veeramani (G-V) setup, which, for our purposes, we consider to be more suitable than Grabiec-completeness. As an important result of our work, we give an original proof for a version of Banach’s fixed-point principle on this particular setup of fuzzy normed spaces, a variant of Jungck’s fixed-point theorem in the same setup, and they are proved in G-V-complete fuzzy normed spaces, paving the way for future developments in various fields within this framework, where our application of dynamic programming makes a proper example. As the uniqueness of almost every dynamic programming problem is necessary, the fixed-point theorems represent an important tool in achieving that goal. |
| first_indexed | 2024-03-09T19:27:04Z |
| format | Article |
| id | doaj.art-ac91aec59a7043dc8cff79bbb1abdd3d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T19:27:04Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ac91aec59a7043dc8cff79bbb1abdd3d2023-11-24T02:49:48ZengMDPI AGSymmetry2073-89942022-09-011410196610.3390/sym14101966Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-ProgrammingTudor Bînzar0Flavius Pater1Sorin Nădăban2Department of Mathematics, Politehnica University of Timişoara, Regina Maria 1, RO-300004 Timişoara, RomaniaDepartment of Mathematics, Politehnica University of Timişoara, Regina Maria 1, RO-300004 Timişoara, RomaniaDepartment of Mathematics and Computer Science, Aurel Vlaicu University of Arad, Elena Drăgoi 2, RO-310330 Arad, RomaniaThe aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed linear spaces as they are defined by Nădăban and Dzitac. When completeness is required, we will use the George and Veeramani (G-V) setup, which, for our purposes, we consider to be more suitable than Grabiec-completeness. As an important result of our work, we give an original proof for a version of Banach’s fixed-point principle on this particular setup of fuzzy normed spaces, a variant of Jungck’s fixed-point theorem in the same setup, and they are proved in G-V-complete fuzzy normed spaces, paving the way for future developments in various fields within this framework, where our application of dynamic programming makes a proper example. As the uniqueness of almost every dynamic programming problem is necessary, the fixed-point theorems represent an important tool in achieving that goal.https://www.mdpi.com/2073-8994/14/10/1966dynamic programmingfixed-point theoremsfuzzy normed linear spaceG-V-completenessfuzzy continuous |
| spellingShingle | Tudor Bînzar Flavius Pater Sorin Nădăban Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming Symmetry dynamic programming fixed-point theorems fuzzy normed linear space G-V-completeness fuzzy continuous |
| title | Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming |
| title_full | Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming |
| title_fullStr | Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming |
| title_full_unstemmed | Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming |
| title_short | Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming |
| title_sort | fixed point theorems in fuzzy normed linear spaces for contractive mappings with applications to dynamic programming |
| topic | dynamic programming fixed-point theorems fuzzy normed linear space G-V-completeness fuzzy continuous |
| url | https://www.mdpi.com/2073-8994/14/10/1966 |
| work_keys_str_mv | AT tudorbinzar fixedpointtheoremsinfuzzynormedlinearspacesforcontractivemappingswithapplicationstodynamicprogramming AT flaviuspater fixedpointtheoremsinfuzzynormedlinearspacesforcontractivemappingswithapplicationstodynamicprogramming AT sorinnadaban fixedpointtheoremsinfuzzynormedlinearspacesforcontractivemappingswithapplicationstodynamicprogramming |