Tensorial Simpson 1/8 Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space

Abstract

Several Simpson 1 8 tensorial type inequalities for selfadjoint operators have been obtained with variation depending on the conditions imposed on the function f
||1/8[f(A)⊗1 + 6f(A⊗1 + 1⊗B/2) + 1⊗f(B)] − ∫₀¹f(λ₁⊗B + (1−λ)A⊗1)dλ|| ≤ 5||1⊗B − A⊗1||/32 ||f’||_I,+∞.