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An affirmative answer to quasi-contraction's open problem under some local constraints in JS-metric spaces

    Sanaz Pourrazi Affiliation
    ; Farshid Khojasteh   Affiliation
    ; Mojgan Javahernia Affiliation
    ; Hasan Khandani Affiliation
DOI: https://doi.org/10.3846/mma.2019.027

Abstract

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. Finally, by taking into account the approximate strict fixed point property we present some worthwhile open problems in these spaces.

Keyword : Iterative fixed point, Strict fixed point, JS-Pompieu Hausdorff, Well-behaved quasi contraction

How to Cite
Pourrazi, S., Khojasteh, F., Javahernia, M., & Khandani, H. (2019). An affirmative answer to quasi-contraction’s open problem under some local constraints in JS-metric spaces. Mathematical Modelling and Analysis, 24(3), 445-456. https://doi.org/10.3846/mma.2019.027
Published in Issue
Jun 6, 2019
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