Functions and Analysis

1811 Submissions

[4] viXra:1811.0496 [pdf] submitted on 2018-11-28 06:20:10

Dieudonné-Type Theorems for Lattice Group-Valued K-Triangular Set Functions

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 19 Pages.

Some versions of Dieudonne-type convergence and uniform boundedness theorems are proved, for k-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case.
Category: Functions and Analysis

[3] viXra:1811.0281 [pdf] submitted on 2018-11-19 04:01:17

Arithmetic of Analysis II

Authors: Fayowole David Ayadi
Comments: 2 Pages.

This work is an alternate method of evaluating absolute (modulus) value.
Category: Functions and Analysis

[2] viXra:1811.0244 [pdf] submitted on 2018-11-15 06:38:41

Remark on the paper of Zheng Jie Sun and Ling Zhu

Authors: Yogesh J. Bagul
Comments: 4 Pages. In this paper , a mathematical mistake is discovered and another simple proof of the theorem is proposed.

In this short review note we show that the new proof of theorem 1.1 given by Zheng Jie Sun and Ling Zhu in the paper Simple proofs of the Cusa-Huygens-type and Becker-Stark-type inequalities is logically incorrect and present another simple proof of the same.
Category: Functions and Analysis

[1] viXra:1811.0222 [pdf] replaced on 2019-10-27 16:08:48

Real Numbers in the Neighborhood of Infinity

Authors: Jonathan W. Tooker
Comments: 32 Pages.

We demonstrate the existence of a broad class of real numbers which are not elements of any number field: those in the neighborhood of infinity. After considering the reals and the affinely extended reals, we prove that numbers in the neighborhood of infinity are ordinary real numbers of the type detailed in Euclid's Elements. We show that real numbers in the neighborhood of infinity obey the Archimedes property of real numbers. The main result is an application in complex analysis. We show that the Riemann zeta function has infinitely many non-trivial zeros off the critical line in the neighborhood of infinity.
Category: Functions and Analysis