On a functional inequality stemming from the Grüss-type inequalities

Abstract

We study functional inequality of the form $$|T(f,h)-T(f,g)T(g,h)|\le F(f,g)F(g,h)-F(f,h)$$ where $T$ is a complex-valued functional and $F$ is a real-valued map. Motivation for our studies comes from some generalizations of Grüss inequality.

References in corpus (2)

• Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces
• Richard's inequality, Cauchy-Schwarz's inequality and approximate solutions of Sincov's equation