Abstract
In this paper, we study two questions of A. Petruşel and G. Petruşel in b-metric fixed point theory [12]. The main results of the paper are as follows.
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(1)
Using the b-metric metrization theorem [9], fixed point results in the setting of b-metric spaces proved in [10,11,12] and some others may be seen as consequences of Ran–Reurings fixed point theorem in the classical metric spaces [13, Theorem 2.1]. This gives a partial answer to the question in [12, Remark 3.(2)].
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(2)
Using the product space of two JS-metric spaces, main results of [12] and some others in the setting of b-metric spaces can be extended to the setting of JS-spaces. This answers the question in [12, Open question on page 1809].
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The authors are greatly indebted to anonymous reviewers for their helpful comments to revise the paper.
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Van Dung, N., Hang, V.T.L. On two questions of A. Petruşel and G. Petruşel in b-metric fixed point theory. J. Fixed Point Theory Appl. 20, 110 (2018). https://doi.org/10.1007/s11784-018-0593-7
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DOI: https://doi.org/10.1007/s11784-018-0593-7