Abstract
We define the multivalued Reich (G; ρ)-contraction mappings on a modular function space. Then we obtain sufficient conditions for the existence of fixed points for such mappings. As an application, we introduce a ρ-valued Bernstein operator on the set of functions f:[0; 1] → Lρand then give the modular analogue to Kelisky-Rivlin theorem.
| Original language | English |
|---|---|
| Pages (from-to) | 4600-4606 |
| Number of pages | 7 |
| Journal | Journal of Nonlinear Science and Applications |
| Volume | 9 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2016 |
Bibliographical note
Publisher Copyright:© 2016 All rights reserved.
Keywords
- Bernstein polynomial
- Directed graph
- Modular function spaces
- Monotone mapping
- Multivalued mapping
- Reich fixed point theorem
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory