Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities

• Autorzy: Judit Makó , Zsolt Páles
• Języki publikacji: EN

Abstrakty

EN

The connection between the functional inequalities $$f\left( {\frac{{x + y}} {2}} \right) \leqslant \frac{{f\left( x \right) + f\left( y \right)}} {2} + \alpha _J \left( {x - y} \right), x,y \in D,$$ and $$\int_0^1 {f\left( {tx + \left( {1 - t} \right)y} \right)\rho \left( t \right)dt \leqslant \lambda f\left( x \right) + \left( {1 - \lambda } \right)f\left( y \right) + \alpha _{\rm H} \left( {x - y} \right),} x,y \in D,$$ 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.

Słowa kluczowe

EN

Convexity; Approximate convexity; Lower and upper Hermite-Hadamard inequalities

Kategorie tematyczne

• 39B12: Iteration theory, iterative and composite equations
• 39B22: Equations for real functions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1017-1041

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Judit Makó

• University of Debrecen

autor

Zsolt Páles

• University of Debrecen

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0027-5