Abstract
In this paper, we prove some common fixed point theorems for order contractive mappings on a σ-complete vector lattice. We apply new results to study the well-posedness of a common fixed point problem for two contractive mappings. Our proofs are simple and purely order-theoretic in nature. Consequently, the shadowing property and Ulam–Hyers stability of a common fixed point problem are studied. The existence of the solution of an integral equation is obtained as an application of our main result.
| Original language | English |
|---|---|
| Article number | 9994453 |
| Journal | Journal of Mathematics |
| Volume | 2025 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2025 |
Keywords
- common fixed point
- limit shadowing property
- order contractive mapping
- Ulam–Hyers stable
- well-posedness
- σ-complete vector lattice
ASJC Scopus subject areas
- General Mathematics