## Rocky Mountain Journal of Mathematics

- Rocky Mountain J. Math.
- Volume 50, Number 2 (2020), 455-466.

### Some inequalities for weighted area balance via functions of bounded variation

Hüseyin Budak and Ebru Pehlivan

#### Abstract

We first define weighted area balance function. Then we prove two identities for the integrable functions involving weighted area balance. Moreover, using these equalities, we obtain some inequalities for mappings of bounded variation and for Lipschitzian functions, respectively.

#### Article information

**Source**

Rocky Mountain J. Math., Volume 50, Number 2 (2020), 455-466.

**Dates**

Received: 25 July 2019

Revised: 2 November 2019

Accepted: 4 November 2019

First available in Project Euclid: 29 May 2020

**Permanent link to this document**

https://projecteuclid.org/euclid.rmjm/1590739282

**Digital Object Identifier**

doi:10.1216/rmj.2020.50.455

**Mathematical Reviews number (MathSciNet)**

MR4104386

**Zentralblatt MATH identifier**

07210971

**Subjects**

Primary: 26D15: Inequalities for sums, series and integrals 26A45: Functions of bounded variation, generalizations

Secondary: 26D10: Inequalities involving derivatives and differential and integral operators

**Keywords**

function of bounded variation Riemann–Stieltjes integrals area balance

#### Citation

Budak, Hüseyin; Pehlivan, Ebru. Some inequalities for weighted area balance via functions of bounded variation. Rocky Mountain J. Math. 50 (2020), no. 2, 455--466. doi:10.1216/rmj.2020.50.455. https://projecteuclid.org/euclid.rmjm/1590739282