SEPARATION THEOREM WITH RESPECT TO SUB-TOPICAL FUNCTIONS AND ABSTRACT CONVEXITY


Authors

M. ALIMOHAMMADY - Department of Mathematics, University of Mazandaran, Babolsar 47416 − 1468, Iran.. A. SHAHMARI - Islamic Azad University, Ayatollah Amoli branch, Amol, Iran.


Abstract

This paper deals with topical and sub-topical functions in a class of ordered Banach spaces. The separation theorem for downward sets and sub-topical functions is given. It is established some best approximation problems by sub-topical functions and we will characterize sub-topical functions as superimum of elementary sub-topical functions.


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