Admissibility of Frechet spaces

• Autorzy: Ciesielski Maciej , Lewicki Grzegorz

Identyfikatory

DOI

10.17512/jamcm.2025.4.01

• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to show the admissibility of some classes of Frechet spaces (see Definition 2.3), which generalizes the particular case given for modular function spaces Eρ. As an application, we show the admissibility of a large class of modular spaces equipped with F-norms, as determined in Theorem 4.1. We also provide applications by proving fixed point theorems in F-admissible spaces (see Theorems 3.5 and 3.6). We would like to add that, in particular, Theorems 3.5 and 3.6 can be applied to find the existence of solutions of integral and differential equations in modular spaces (see Theorem 4.7, Remark 4.8 and Remark 4.9). It is worth noticing that F-norms introduced in Theorem 4.1 generalize the classical Luxemburg F-norm.

Słowa kluczowe

EN

admissible space; modular function spaces; Frechet spaces; fixed point theory

PL

przestrzeń dopuszczalna; przestrzeń funkcyjna modularna; przestrzeń Frecheta; teoria punktów stałych

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 4
• Strony: 5--25
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Ciesielski Maciej

• Institute of Mathematics, Poznan University of Technology Poznań, Poland

autor

Lewicki Grzegorz

• Department of Mathematics and Computer Science, Jagiellonian University Kraków, Poland

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).