AN AFFIRMATIVE ANSWER TO QUASI-CONTRACTION'S OPEN PROBLEM UNDER SOME LOCAL CONSTRAINTS IN JS-METRIC SPACES

Sanaz Pourrazi, Farshid Khojasteh, Mojgan Javahernia, Hasan Khandani
2019 Mathematical Modelling and Analysis  
In this work, we first present JS-Pompeiu-Hausdorff metric in JS metric spaces and then introduce well-behaved quasi-contraction in order to find an affirmative answer to quasi-contractions' open problem under some local constraints in JS-metric spaces. In the literature, this problem solved when the constant modules α ∈ [0,1/2] and when α ∈ (1/2,1], finding conditions by which the set of all fixed points be non-empty, has remained open yet. Moreover, we support our result by a notable example.
more » ... a notable example. Finally, by taking into account the approximate strict fixed point property we present some worthwhile open problems in these spaces.
doi:10.3846/mma.2019.027 fatcat:s6h6shu6srhhzlviguutga6t7i