Related papers: A refinement of a theorem by Franks

We obtain some results related to Romanoff's theorem.

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

The aim of the present paper is to give extensions of the cosine-sine functional equation.

A refinement of the Hardy inequality has been presented by use of superquadratic function.

We prove two single-parameter q-supercongruences which were recently conjectured by Guo, and establish their further extensions with one more parameter. Crucial ingredients in the proof are the terminating form of q-binomial theorem and a…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.

In his recent work, Andrews revisited two-color partitions with certain restrictions on the differences between consecutive parts, and he established three theorems linking these two-color partitions with more familiar kinds of partitions.…

Under a slightly stronger hypothesis, one improves a connectedness result of Debarre [D] for a product of two projective spaces in terms of the extension problem of formal-rational functions (see Theorems 1.3 and 1.4 of the introduction)

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.

In this article we use the Desargues' theorem and its reciprocal to solve two problems.

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We prove some extensions of Andrews inequality.

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.