Fixed points for singlevalued operators with respect to tau-distance

In this paper we first recall the concept of tau-distance on a metric space. Then, we prove a fixed point theorem for singlevalued operators in terms of a tau-distance.fixed point, tau-distance, singlevalued operator

On Principal Fuzzy Metric Spaces

[EN] In this paper, we deal with the notion of fuzzy metric space (X, M, *), or simply X, due to George and Veeramani. It is well known that such fuzzy metric spaces, in general, are not completable and also that there exist p-Cauchy sequences which are not Cauchy. We prove that if every p-Cauchy sequence in X is Cauchy, then X is principal, and we observe that the converse is false, in general. Hence, we introduce and study a stronger concept than principal, called strongly principal. Moreover, X is called weak p-complete if every p-Cauchy sequence is p-convergent. We prove that if X is strongly principal (or weak p-complete principal), then the family of p-Cauchy sequences agrees with the family of Cauchy sequences. Among other results related to completeness, we prove that every strongly principal fuzzy metric space where M is strong with respect to an integral (positive) t-norm * admits completion.Samuel Morillas acknowledges financial support from Ministerio de Ciencia e Innovacion of Spain under grant PID2019-107790RB-C22 funded by MCIN/AEI/10.13039/501100011033. JuanJose Minana acknowledges financial support from Proyecto PGC2018-095709-B-C21 financiado por MCIN/AEI/10.13039/501100011033 y FEDER "Una manera de hacer Europa" and from project BUGWRIGHT2. This last project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 871260. Also acknowledge support of Generalitat Valenciana under grant CIAICO/2021/137. This publication reflects only the authors' views and the European Union is not liable for any use that may be made of the information contained therein.Gregori Gregori, V.; Miñana, J.; Morillas, S.; Sapena Piera, A. (2022). On Principal Fuzzy Metric Spaces. Mathematics. 10(16):1-10. https://doi.org/10.3390/math10162860110101

Extensions and applications of ACF mappings

Using a definition of ASF sequences derived from the definition of asymptotic contractions of the final type of ACF, we give some new fixed points theorem for cyclic mappings and alternating mapping which extend results from T.Suzuki and X.Zhang

Weak Compatibility and Common Fixed Point Theorems for A-Contractive and E-expansive Maps in Uniform Spaces

2000 Mathematics Subject Classification: 47H10, 54E15.The purpose of this paper is to define the notion of A-distance and E-distance in uniform spaces and give several new common fixed point results for weakly compatible contractive or expansive selfmappings of uniform spaces