A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces Zhou, Mi Saleem, Naeem Liu, Xiaolan Fulga, Andreea Roldán López de Hierro, Antonio Francisco Fuzzy metric space Fixed point Proinov-type contraction Non-Archimedean fuzzy metric space Very recently, by considering a self-mapping T on a complete metric space satisfying a general contractivity condition of the form ψ(d(Tx, Ty)) ≤ ϕ(d(x, y)), Proinov proved some fixedpoint theorems, which extended and unified many existing results in the literature. Accordingly, inspired by Proinov-type contraction conditions, Roldán López de Hierro et al. introduced a novel family of contractions in fuzzy metric spaces (in the sense of George and Veeramani), whose main advantage is the very weak constraints imposed on the auxiliary functions that appear in the contractivity condition. They also proved the existence and uniqueness of fixed points for the discussed family of fuzzy contractions in the setting of non-Archimedean fuzzy metric spaces. In this paper, we introduce a new family of fuzzy contractions based on Proinov-type contractions for which the involved auxiliary functions are not supposed to satisfy any monotonicity assumptions; further, we establish some new results about the existence and uniqueness of fixed points. Furthermore, we show how the main results in the above-mentioned paper can be deduced from our main statements. In this way, our conclusions provide a positive partial solution to one of the open problems posed by such authors for deleting or weakening the hypothesis of the nondecreasingness character of the auxiliary functions. 2021-11-24T11:53:36Z 2021-11-24T11:53:36Z 2021 info:eu-repo/semantics/article Zhou, M.; Saleem, N.; Liu, X.; Fulga, A.; Roldán López de Hierro, A.F. A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces. Mathematics 2021, 9, 3001. https://doi.org/ 10.3390/math9233001 http://hdl.handle.net/10481/71719 10.3390/math9233001 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI