On Popoviciu-Ionescu Functional Equation

On Hilbert Golab-Schinzel type functional equation

Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...

Hlawka–Popoviciu inequalities on positive definite tensors

Article history: Received 13 November 2014 Accepted 25 August 2015 Available online xxxx Submitted by V. Mehrmann MSC: 15A15 15A39 15A69 46M05 47A63

ON THE LIFTING PROPERTY. Il l BY A. IONESCU TULCEA AND C. IONESCU TULCEA

1. Let Z be a locally compact space and / i ^ O a positive Radon measure on Z. Let MR(Z} /X) be the Banach algebra of all bounded real-valued /x-measurable functions defined on Z, endowed with the norm/—»||/||oo = sup2 G^|/(0)| . Let CR(Z) be the subalgebraof MR{Z,\X) consisting of all bounded continuous functions on Z and 3C(Z) the subalgebra of all ƒ G CR (Z) having compact support. For two f...

Stability of additive functional equation on discrete quantum semigroups

We construct  a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...

On the Stability of the Orthogonally Quartic Functional Equation