Abstract
In this paper, we present a class of functions:f:X→
such that inf x∈X f(x)=\(\inf _{x \in {\rm B}_X } f(x)\), whereX is a nonempty, finitely compact and convex set in a vector space andB x ={x∈X: ∃y∈ aff(X)∖{x:[x, y]∩X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1).
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Ricceri, B.,Some Topological Minimax Theorems via an Alternative Principle for Multifunctions, Archiv der Mathematik, Vol. 60, pp. 367–377, 1993.
Roberts, A. W., andVarberg, D. E.,Convex Functions, Academic Press, New York, New York, 1973.
Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer Verlag, New York, New York, 1975.
Aubin, J. P., andEkeland, I.,Applied Nonlinear Analysis, John Wiley and Sons, New York, New York, 1984.
Kelly, P. J., andWeiss, M. L.,Geometry and Convexity, John Wiley and Sons, New York, New York, 1979.
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Communicated by R. Conti
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Naselli, O. On a class of functions with equal infima over a domain and its boundary. J Optim Theory Appl 91, 81–90 (1996). https://doi.org/10.1007/BF02192283
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DOI: https://doi.org/10.1007/BF02192283