## Real Analysis Exchange

### A Generalization of the Fundamental Theorem of Calculus

Keqin Liu

#### Abstract

After introducing the concepts of $\varphi$-derivatives and $\varphi$-integrals inside the dual real number algebra, we prove a new generalization of the fundamental theorem of calculus.

#### Article information

Source
Real Anal. Exchange, Volume 39, Number 1 (2013), 239-260.

Dates
First available in Project Euclid: 1 July 2014

https://projecteuclid.org/euclid.rae/1404230150

Mathematical Reviews number (MathSciNet)
MR3261909

Zentralblatt MATH identifier
1298.26038

Subjects
Primary: 26A99: None of the above, but in this section

#### Citation

Liu, Keqin. A Generalization of the Fundamental Theorem of Calculus. Real Anal. Exchange 39 (2013), no. 1, 239--260. https://projecteuclid.org/euclid.rae/1404230150