Inequalities

Sufficient Inequalities for Univalent Functions

In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

Concentration inequalities and martingale inequalities — a survey

We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and webgraphs.

Height inequalities and canonical class inequalities

This lecture is concerned with apriori bounds on the size of solutions to Diophantine equations. We will present a rather random collection of results with the intention to provide a flavor of the subject, with only a glimpse of something like a unifying principle. In the next lecture, we will make a better attempt to give coherence to our exposition, by describing the relation to canonical cla...

Modified logarithmic Sobolev inequalities and transportation inequalities

New integral inequalities for $s$-preinvex functions

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.