Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

This paper deals with the question of achieving a suitable extension notion Suzuki-type contraction to framework quasi-metric spaces, which allows us obtain reasonable fixed point theorems in context. has no an easy answer; fact, we here present example self map Smyth complete space (a very strong kind completeness) that fulfills simple and natural but does not have points. Despite it, implement approach two results, whose validity is supported several examples. Finally, general method construct non-T1 spaces such way it possible systematically generate non-Banach contractions are Suzuki-type. Thus, can apply our results deduce existence uniqueness solution for some kinds functional equations exemplified distinguished case.