2021/11/26 by В. Ф. Бабенко, Babenko, Vladyslav, Vira Babenko +3
Mathematics · #47H09 #47H10 #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2111.13625
openalex publication_date 2021/11/26 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including metric and uniform spaces. On the other hand, compared to the so-called cone metric spaces and K-metric spaces, we do not require that the distance function range has a linear structure. We also consider several applications of the obtained fixed point theorems. In particular, we consider the questions of the existence of solutions of the Fredholm integral equation in L-spaces.