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Best proximity pair theorem in metrizable topological vector spaces

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Analysis in Theory and Applications

Abstract

The object of this paper is to prove an existence result on best proximity pair. For this purpose, the class of factorizable multifunctions in approximately weakly compact, convex subset of metrizable topological vector space is used. As consequence, our theorem generalizes the result of Basha and Veeramani[10]. Finally, certain known results have also been obtained as corollaries in this work.

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Authors and Affiliations

  1. School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, 492010, Chhattisgarh, India

    H. K. Nashine & C. L. Dewangan

  2. Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg(Baloda Bazar Road), Mandir Hasaud, Raipur, 492101, Chhattisgarh, India

    H. K. Nashine

  3. Faculty of Electrical Engineering Department of Mathematics, University of Banja Luka, Parte 5, 78000, Banja Luka, Bosnia and Herzegovina, Yugoslavia

    Z. D. Mitrovic

Authors
  1. H. K. Nashine
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  2. C. L. Dewangan
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  3. Z. D. Mitrovic
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Correspondence to H. K. Nashine.

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Nashine, H.K., Dewangan, C.L. & Mitrovic, Z.D. Best proximity pair theorem in metrizable topological vector spaces. Anal. Theory Appl. 26, 59–68 (2010). https://doi.org/10.1007/s10496-010-0059-2

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  • DOI: https://doi.org/10.1007/s10496-010-0059-2

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