Abstract
We prove the existence of fixed points of monotone ρ-nonexpansive mappings in ρ-uniformly convex modular function spaces. This is the modular version of Browder and Göhde fixed point theorems for monotone mappings. We also discuss the validity of this result in modular function spaces where the modular is uniformly convex in every direction. This property has never been considered in the context of modular spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 5219-5228 |
| Number of pages | 10 |
| Journal | Journal of Nonlinear Science and Applications |
| Volume | 9 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2016 |
Bibliographical note
Publisher Copyright:© 2016 All rights reserved.
Keywords
- Fixed point
- Krasnoselskii iteration
- Modular function spaces
- Monotone mapping
- Nonexpansive mapping
- Partially ordered
- Uniformly convex
- Uniformly convex in every direction
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory