Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...
Abstract.The purpose of this paper is to prove that the functions generated by the integral operator I(f,g)(z)= ∫ 0 z ∏ i=1 n ( f i (t) g i (t) ) γ i 𝑑𝑡 are in the class of close-to-convex functions ...
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