Related papers: A note on certain inequalities for bivariate means

By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

This short note contains elementary evaluations of some Euler sums.

The note contains a short elementary proof of Cayley's formula for labeled trees.

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

This note proves a version of Lubell-Yamamoto-Meshalkin inequality for general product measures.

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

This note gives a short proof on characterizations of a forest to be equitably k-colorable.

We obtain variational inequalities for some classes of bilinear averages of one variable, generalizing the variational inequalities for averages of R. Jones {\it et al}. As an application we get almost everywhere convergence for the ergodic…

In this short note, we obtain error estimates for Riemann sums of some singular functions.

In this paper, we gave some properties of binomial coefficient.

We determine the asymptotic behaviour of certain incomplete Betafunctions.

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…

In this note, we derive a Leibniz rule for difference quotient.

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert,…

In this note we briefly survey and propose some open problems related to isoparametric theory.

These notes are a self-contained short proof of the stability of persistence diagrams.

We prove two local inequalities for divisors on surfaces and study their applications.