Abstract
In this article, we introduce and study the concept of hyperconvexity (which we call \(q^\lambda \)-hyperconvexity) that is appropriate in the category of \(T_0\)-quasi-metric spaces and nonexpansive maps and this will generalize the notion of q-hyperconvexity studied by Kemajou et al. We prove a fixed point result for nonexpansive maps in \(q^\lambda \)-hyperconvex spaces and establish, among other things, that the fixed point set of nonexpansive maps on \(q^\lambda \)-hyperconvex bounded \(T_0\)-quasi-metric spaces is itself \(q^\lambda \)-hyperconvex.
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Notes
This just means that \(T_i(T_j(x))=T_j(T_i(x))\) whenever \(i,j\in I\) and \(x\in X.\)
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The first author would like to thank Nelson Mandela University for partial financial support and the National Research Foundation of South Africa for partial financial support under grant 115223.
The second author would like to acknowledge the TWAS-DFG Cooperation Programme for full funding received for a research stay during winter 2017 at Universitat der Bundeswehr Munchen in Prof. Dr. Vasco Brattka’s lab, in Germany and during which the paper was completed. This research was also supported by the government of Canada’s International Development Research Centre (IDRC) and within the framework of the AIMS Research for Africa Project.
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Agyingi, C.A., Gaba, Y.U. \(q^\lambda \)-hyperconvexity in quasi-metric spaces. Afr. Mat. 30, 399–412 (2019). https://doi.org/10.1007/s13370-019-00656-5
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DOI: https://doi.org/10.1007/s13370-019-00656-5