Some results on best proximity pair theorems

P.S. Srinivasan; P. Veeramani

doi:10.4995/agt.2002.2109

Authors

P.S. Srinivasan Indian Institute of Technology
P. Veeramani Indian Institute of Technology Madras

DOI:

https://doi.org/10.4995/agt.2002.2109

Keywords:

Best proximity pairs, Kakutani multifunctions, Simplicial approximations, Best approximations

Abstract

Best proximity pair theorems are considered to expound the sufficient conditions that ensure the existence of an element x_o ϵ A, such that

d(x_o; T x_o) = d(A;B)

where T : A 2^B is a multifunction defined on suitable subsets A and B of a normed linear space E. The purpose of this paper is to obtain best proximity pair theorems directly without using any multivalued fixed point theorem. In fact, the well known Kakutani's fixed point theorem is obtained as a corollary to the main result of this paper.

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Author Biographies

P.S. Srinivasan, Indian Institute of Technology

Department of Mathematics

Indian Institute of Technology

Madras, Chennai600 036, India

P. Veeramani, Indian Institute of Technology Madras

Department of Mathematics

Indian Institute of Technology

Madras, Chennai600 036, India

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