Generalizations on contractive mappings in metric spaces

We present new results on generalizations on metric spaces. New results are given on contractions in metric spaces and their fuzzy sets

Function Spaces, Hyperspaces, and Asymmetric and Fuzzy Structures

Romaguera Bonilla, S.; Beer, G.; Sanchis, M. (2013). Function Spaces, Hyperspaces, and Asymmetric and Fuzzy Structures. Journal of Function Spaces and Applications. doi:10.1155/2013/619707

Rational Contractions in b-Metric Spaces

In this paper, we prove fixed point theorems for contractions and generalized weak contractions satisfying rational expressions in complete b-metric spaces. Our results generalize several well-known comparable results in the literature

Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

[EN] Involving w-distances we prove a fixed point theorem of Caristi-type in the realm of (non -necessarily T-1) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non-T-1 quasi-metric spaces. As an application, we deduce a characterization of complete G-metric spaces in terms of a weak version of Caristi's theorem that involves a G-metric version of w-distances.Karapinar, E.; Romaguera Bonilla, S.; Tirado Peláez, P. (2022). Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points. Demonstratio Mathematica (Online). 55(1):939-951. https://doi.org/10.1515/dema-2022-017793995155

On the order type L-valued relations on L-powersets

The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc.) on an ordinary set $X$, while $L$-valued sets $X$ (that are sets equipped with some $L$-valued equalities $E: X\times X \to L$, or, more generally, with $L$-valued relations $R: X \times X \to L$) are the starting point for the second one. ($L$ being a lattice usually with an additionally algebraic structure). The aim of this work is to discuss the problem how an $L$-valued relation given on a set $X$ can be extended to the $L$-valued relation $\R$ on the $L$-powerset $L^X$. This problem, is important, among other for the theory of $L$-fuzzy topological spaces in the sense of [15], [16].Peer Reviewe