Abstract
In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the original norm of the normed linear space X is presented.
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Acknowledgements
The authors are very grateful to the anonymous referee for his/her useful suggestions regarding an earlier version of this paper. The comments of the referee were very useful and they helped us to improve the paper significantly. This research was partially supported by Mahani Mathematical Research Center.
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Barsam, H., Mohebi, H. On non-expansivity of topical functions by a new pseudo-metric. Arab. J. Math. 9, 49–62 (2020). https://doi.org/10.1007/s40065-018-0222-8
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DOI: https://doi.org/10.1007/s40065-018-0222-8