Related papers: A higher order Weierstrass approximation theorem -…

An introduction and survey of homotopy type theory in honor of W.W. Tait.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

In this note we shall give a new proof to a quadrature formulae due to Newton.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We describe recent advances in the study of random analogues of combinatorial theorems.

A very simple but useful almost sure convergence theorem of probability is given.

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…

In this note a far extension of the Banach fixed point theorem is proved.

In this note we give a detailed proof of a theorem of Aubin.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

We prove a continued fraction expansion for the reciprocal of a certain $q$-series. All the specialists in the world are asked whether it is new or not.

The aim of the present article is to extend the Stone--Weierstrass theorem to functions ranging in a lattice normed space and order rather than topological approximation. We proceed with the machinery of Boolean valued transfer from lattice…

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…

We show a new large sieve version of the Brun-Titchmarsh theorem.

We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

We proove a Bloch's theorem in an almost complex projective plane.