Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of Đ. 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. © Işık University, Department of Mathematics, 2023; all rights reserved.
Кључне речи:
F-contraction / Fixed point / fractional differential equation / Perov type / pseudometric / vector-valued metricИзвор:
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 2023, 13, 3, 880-890Финансирање / пројекти:
- Ministry of Education, Science and Technological Development of the Republic of Serbia
Институција/група
VinčaTY - JOUR AU - Fabiano, Nicola AU - Kadelburg, Zoran AU - Mirkov, Nikola S. AU - Radenović, Stojan PY - 2023 UR - https://vinar.vin.bg.ac.rs/handle/123456789/11360 AB - In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of Đ. 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. © Işık University, Department of Mathematics, 2023; all rights reserved. T2 - Turkish World Mathematical Society Journal of Applied and Engineering Mathematics T1 - Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type VL - 13 IS - 3 SP - 880 EP - 890 UR - https://hdl.handle.net/21.15107/rcub_vinar_11360 ER -
@article{ author = "Fabiano, Nicola and Kadelburg, Zoran and Mirkov, Nikola S. and Radenović, Stojan", year = "2023", abstract = "In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of Đ. 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. © Işık University, Department of Mathematics, 2023; all rights reserved.", journal = "Turkish World Mathematical Society Journal of Applied and Engineering Mathematics", title = "Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type", volume = "13", number = "3", pages = "880-890", url = "https://hdl.handle.net/21.15107/rcub_vinar_11360" }
Fabiano, N., Kadelburg, Z., Mirkov, N. S.,& Radenović, S.. (2023). Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type. in Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 13(3), 880-890. https://hdl.handle.net/21.15107/rcub_vinar_11360
Fabiano N, Kadelburg Z, Mirkov NS, Radenović S. Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type. in Turkish World Mathematical Society Journal of Applied and Engineering Mathematics. 2023;13(3):880-890. https://hdl.handle.net/21.15107/rcub_vinar_11360 .
Fabiano, Nicola, Kadelburg, Zoran, Mirkov, Nikola S., Radenović, Stojan, "Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type" in Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 13, no. 3 (2023):880-890, https://hdl.handle.net/21.15107/rcub_vinar_11360 .