Displaying similar documents to “The existence of a solution of a nonlinear boundary value problem”

Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities

Judit Makó, Zsolt Páles (2012)

Open Mathematics

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The connection between the functional inequalities f x + y 2 ⩽ f x + f y 2 + α J x - y , x , y ∈ D , and ∫ 0 1 f t x + 1 - t y ρ t d t ⩽ λ f x + 1 - λ f y + α H x - y , x , y ∈ D , is investigated, where D is a convex subset of a linear space, f: D → ℝ, α H;α J: D-D → ℝ are even functions, λ ∈ [0; 1], and ρ: [0; 1] →ℝ+ is an integrable nonnegative function with ∫01 ρ(t) dt = 1.