SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS USING FIXED POINT RESULTS IN GENERALIZED METRIC SPACES OF PEROV'S TYPE
In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the r...
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| Published in | TWMS journal of applied and engineering mathematics Vol. 13; no. 3; p. 880 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Istanbul
Turkic World Mathematical Society
01.01.2023
Elman Hasanoglu |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2146-1147 2146-1147 |
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| Abstract | In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. Keywords: Fixed point; vector-valued metric, pseudometric; Perov type; F-contraction; fractional differential equation. AMS Subject Classification: Primary 47H10; Secondary 54H25, 35A08. |
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| AbstractList | In 1964, A. I. Perov generalized the Banach contraction principle intro- ducing, following the work of ̄D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and pro- viding some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this ar- ticle some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. Keywords: Fixed point; vector-valued metric, pseudometric; Perov type; F-contraction; fractional differential equation. AMS Subject Classification: Primary 47H10; Secondary 54H25, 35A08. In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. |
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| Author | Kadelburg, Z Fabiano, N Radenovic, S Mirkov, N |
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| Copyright | COPYRIGHT 2023 Turkic World Mathematical Society 2023. This work is licensed under http://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Snippet | In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of D. Kurepa, a new approach to fixed point problems, by... In 1964, A. I. Perov generalized the Banach contraction principle intro- ducing, following the work of ̄D. Kurepa, a new approach to fixed point problems, by... |
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| SubjectTerms | Differential equations Fractional calculus Mathematicians Mathematics Metric space Theorems |
| Title | SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS USING FIXED POINT RESULTS IN GENERALIZED METRIC SPACES OF PEROV'S TYPE |
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