Geodesic
Some Hermite–Hadamard type inequalities for the square norm in Hilbert spaces
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 75 (2021) no. 2, pp. 31-44.

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Let ( H;〈· ,·〉) be a complex Hilbert space and f:[0,∞ )→ℝ be convex (concave) on [0,∞ ). If x, y∈ H with Re 〈 x,y〉≥ 0, then f( ‖ x‖ ^2+Re 〈 x,y〉 +‖ y‖ ^2/3) ≤( ≥) ∫_0^1f( ‖( 1-t) x+ty‖^2) dt ≤( ≥) 1/3[ f( ‖ x‖^2) +f[ Re 〈 x,y〉] +f(‖ y‖ ^2) ] . Some examples for power functions and exponential are also provided.
Keywords: Convex functions, Hermite–Hadamard inequality, midpoint inequality, power and exponential functions 
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Dragomir, Silvestru Sever. Some Hermite–Hadamard type inequalities for the square norm in Hilbert spaces. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 75 (2021) no. 2, pp. 31-44. http://geodesic.mathdoc.fr/item/AUM_2021_75_2_a2/

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