Faculty of Science, University of Novi Sad, Trg Dositeja Obradovića 3, 21000 Novi Sad, Serbia

Mathematics, College of Sport Health and Engineering, Victoria University Melbourne City, VIC 8001, Australia

link: https://doi.org/10.28924/ada/ma.4.17

Authors:

Vuk Stojiljković

Sever Silvestru Dragomir

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Intro

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,+∞.

The concept we now call a "tensor" wasn’t originally named that way. When Josiah Willard Gibbsfirst described the idea in the late 19th century, he used the term "dyadic." Today, mathematicians define a tensor as the mathematical embodiment of Gibbs’ initial concept. Tensors and inequalitiesare natural partners, thanks to the widespread use of inequalities in mathematics. These mathemat-ical statements about comparisons have a profound impact on various scientific disciplines. Whilemany types of inequalities exist, some of the most significant ones include Jensen’s, Ostrowski’s,Hermite-Hadamard’s, and Minkowski’s inequalities.

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