Related papers: A higher order Weierstrass approximation theorem -…

The celebrated and famous Weierstrass approximation theorem characterizes the set of continuous functions on a compact interval via uniform approximation by algebraic polynomials. This theorem is the first significant result in…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

We give a new simpler proof of a theorem of Jayne and Rogers.

The aim of this paper is to prove characterization theorems for higher order derivations. Among others we prove that the system defining higher order derivations is stable. Further characterization theorems in the spirit of N.~G.~de Bruijn…

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

We present a generalization of a formula of higher order derivatives and give a short proof.

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

In this expository note we give proof of the Weierstrass gap theorem in Cohomology terminology. We analyze gap sequence for finding possible gaps and non-gaps on X.

Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.

We improve the previuosly known bound for some vertex Folkman numbers.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We give a new proof of Lucas' Theorem in elementary number theory.

We present a new, elementary, dynamical proof of the prime number theorem.

A proof is given of Rosenthal's \(\ell_1\) theorem.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

A vector variational principle is proved.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…