On Strong ( Α , F ) – Convexity
نویسندگان
چکیده
In this paper, strongly (α ,T ) -convex functions, i.e., functions f : D → R satisfying the functional inequality f (tx+(1− t)y) t f (x)+(1− t) f (y)− tα(1− t)(x− y)− (1− t)αt(y− x) for x,y ∈ D and t ∈ T ∩ [0,1] are investigated. Here D is a convex set in a linear space, α is a nonnegative function on D−D , and T ⊆ R is a nonempty set. The main results provide various characterizations of strong (α ,T ) -convexity in the case when T is a subfield of R . Mathematics subject classification (2010): Primary 39B62, 26B25.
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