László Losonczi

Minkowski's inequality for two variable difference means

We study Minkowski’s inequality Da b(x1 + x2, y1 + y2) ≤ Da b(x1, y1) +Da b(x2, y2) (x1, x2, y1, y2 ∈ R+) and its reverse where Da b is the difference mean introduced by Stolarsky. We give necessary and sufficient conditions (concerning the parameters a, b) for the inequality above (and for its reverse) to hold.

On the stability of Hosszú’s functional equation

Two stability results are proved. The first one states that Hosszú’s functional equation % MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXanrfitLxBI9gBaerbd9wDYLwzYbItLDharqqt% ubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq% -Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0x% fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuam% aaBaaaleaacaaIXaGaaGimaaqabaGccqGH9aqpciGGSbGaaiOBaiaa% ysW7caWGRbWaaSbaaSqaaiaadsfacaaIXaaabeaakiaac+cacaWGRb% WaaSbaaSqaaiaadsfacaaIYaaabeaakiabg2da9iabgkHiTmaabmaa% baGaamyramaaBaaaleaacaWGHbaabeaakiaac+cacaWGsbaacaGLOa% GaayzkaaGaey41aq7aaiWaaeaadaqadaqaaiaadsfadaWgaaWcbaGa% aGOmaaqabaGccqGHsislcaWGubWaaSbaaSqaaiaaigdaaeqaaaGcca% GLOaGaayzkaaGaai4laiaacIcacaWGubWaaSbaaSqaaiaaikdaaeqa% aOGaaGjbVlaadsfadaWgaaWcbaGaamysaaqabaGccaGGPaaacaGL7b% GaayzFaaaaaa!5C4A!

An extension theorem

f(x+y-xy)+f(xy)=f(x)-f(y)=0\ \ \ \ \ (x,y \in \rm R)

Hölder-Type Inequalities

is stable. The second is a local stability theorem for additive functions in a Banach space setting.

The Behaviour of Comprehensive Classes of Means Under Equal Increments of Their Variables

Inequalities of the form

A structure theorem for sum form functional equations

\alpha \sum\limits_{{\text{j = 0}}}^{\text{n}} {{\text{|}}{{\text{X}}_{\text{j}}}{{\text{|}}^{\text{2}}} \leqslant \sum {{\text{|}}{{\text{X}}_{\text{j}}} \pm {{\text{X}}_{\text{j}}}{\text{ + k}}{{\text{|}}^{\text{2}}} \leqslant \beta \sum\limits_{{\text{j = 0}}}^{\text{n}} {{\text{|}}{{\text{X}}_{\text{j}}}{{\text{|}}^{\text{2}}}} } }