We present an extension of Fenchel’s duality theorem to nearly convexity, giving weaker conditions under which it takes place. Instead of minimizing the difference between a convex and a concave function, we minimize the subtraction of a nearly concave function from a nearly convex one. The assertion in the special case of Fenchel’s duality theorem that consists in minimizing the difference bet...

The present review paper provides recent results on convexity and its applications to the constrained extension of linear operators, motivated by existence subgradients continuous convex Markov moment problem related approximation using Krein–Milman theorem, optimization, polynomial unbounded subsets. In many cases, Mazur–Orlicz theorem also leads operators as solutions. common point all these ...

The main object of this paper is to introduce and investigate a subclass U(λ, α, β, k) of normalized analytic functions in the open unit disk ∆, which generalizes the familiar class of uniformly convex functions. The various properties and characteristics for functions belonging to the class U(λ, α, β, k) derived here include (for example) a characterization theorem, coefficient inequalities an...