Polynomial-like iterative equation on Riesz spaces

Authors

Chaitanya Gopalakrishna, Indian Statistical Institute Bangalore
Weinian Zhang, Sichuan University

Article Type

Research Article

Publication Title

Positivity

Abstract

In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to R and Rⁿ, special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed.

DOI

10.1007/s11117-024-01072-1

Publication Date

9-1-2024

Recommended Citation

Gopalakrishna, Chaitanya and Zhang, Weinian, "Polynomial-like iterative equation on Riesz spaces" (2024). Journal Articles. 4988.
https://digitalcommons.isical.ac.in/journal-articles/4988