A New Approach to Proinov-Type Fixed-Point Results in Non-Archimedean Fuzzy Metric Spaces

Very recently, by considering a self-mapping T on complete metric space satisfying general contractivity condition of the form ψ(d(Tx,Ty))≤φ(d(x,y)), Proinov proved some fixed-point theorems, which extended and unified many existing results in literature. Accordingly, inspired Proinov-type contraction conditions, Roldán López de Hierro et al. introduced novel family contractions fuzzy spaces (in sense George Veeramani), whose main advantage is very weak constraints imposed auxiliary functions that appear condition. They also existence uniqueness fixed points for discussed setting non-Archimedean spaces. In this paper, we introduce new based involved are not supposed to satisfy any monotonicity assumptions; further, establish about points. Furthermore, show how above-mentioned paper can be deduced from our statements. way, conclusions provide positive partial solution one open problems posed such authors deleting or weakening hypothesis nondecreasingness character functions.