arXiv subjects

Slavko Simić

Publications and source records attributed to Slavko Simić.

5 recordsLinked to original sources

arXiv2013

Sharp Lipschitz constants for the distance ratio metric

We study expansion/contraction properties of some common classes of mappings of the Euclidean space ${\mathbb R}^n, n\ge 2\,,$ with respect to the distance ratio metric. The first main case is the behavior of Möbius transformations of the unit ball in ${\mathbb R}^n$ onto itself. In the second main case we study the polynomials of the unit disk onto a subdomain of the complex plane. In both cases sharp Lipschitz constants are obtained.

math.CV↗

arXiv2013

Lipschitz conditions and the distance ratio metric

We give study the Lipschitz continuity of Möbius transformations of a punctured disk onto another punctured disk with respect to the distance ratio metric.

math.MG↗

arXiv2012

Bernoulli inequality and hypergeometric functions

Bernoulli type inequalities for functions of logarithmic type are given. These functions include, in particular, Gaussian hypergeometric functions in the zero-balanced case $F(a,b;a+b;x)\,.$

math.CA↗

arXiv2011

Landen inequalities for zero-balanced hypergeometric functions

For zero-balanced Gaussian hypergeometric functions $ F(a,b;a+b;x),$ $a,b>0,$ we determine maximal regions of $ab$ plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each $x\in (0,1)$. Thereby an exhausting answer is given to an open problem.

math.CA↗

arXiv2011

On quotients and differences of hypergeometric functions

For Gaussian hypergeometric functions $F(x)= F(a,b;c;x),$ $a,b,c>0,$ we consider the quotient $ Q_F(x,y)= (F(x)+F(y))/F(z)$ and the difference $ D_F(x,y)= F(x)+F(y)-F(z)$ for $0<x,y<1$ with $z=x+y-xy \,.$ We give best possible bounds for both expressions under various hypotheses about the parameter triple $(a,b;c)\,.$

math.CA↗