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Riemann-Stieltjes Integral [PDF]

Formalized Mathematics, 2016
In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we
Nakasho, Kazuhisa, Narita, Keiko, Shidama, Yasunari   +2 more
core   +6 more sources

On interval-valued $\mathbb{K}$-Riemann integral and Hermite-Hadamard type inequalities

AIMS Mathematics, 2021
We introduce the concepts of $\mathbb{K}$-Riemann integral and radial $\mathbb{K}$-g$H$-derivative for interval-valued functions. We also give some important properties of interval-valued $\mathbb{K}$-Riemann integral, and extend interval-valued Hermite ...
Zehao Sha, Guoju Ye, Dafang Zhao, Wei Liu   +3 more
doaj   +1 more source

On the Riemann-Stieltjes Integral [PDF]

Mathematics Interdisciplinary Research, 2022
This study contributes to the theory of Riemann-Stieltjes integral. We prove that if all continuous piecewise linear functions are Riemann-Stieltjes integrable with respect to a bounded integrator α : [a,b] → R, then α must be of bounded variation on [a ...
Ali Parsian
doaj   +1 more source

New Hermite-Hadamard inequalities in fuzzy-interval fractional calculus via exponentially convex fuzzy interval-valued function

AIMS Mathematics, 2021
In the present note, we develop Hermite-Hadamard type inequality and He's inequality for exponential type convex fuzzy interval-valued functions via fuzzy Riemann-Liouville fractional integral and fuzzy He's fractional integral.
Yanping Yang, Muhammad Shoaib Saleem, Waqas Nazeer, Ahsan Fareed Shah   +3 more
doaj   +1 more source

Riemann integral and its relation with Lebesgue integral

Bibechana, 2010
This review explains the limitations of the Riemann integral and focuses on the more general concept. It has been suggested that a better route is to abandon the Riemann integral for Lebesgue integral and explained the importance of Lebesgue integral in ...
Mani Raj Bhattrai
doaj   +3 more sources

Equivalences of Riemann Integral Based on p-Norm

Mathematics, 2018
In the usual Riemann integral setting, the Riemann norm or a mesh is adopted for Riemann sums. In this article, we use the p-norm to define the p-integral and show the equivalences between the Riemann integral and the p-integral.
Ray-Ming Chen
doaj   +1 more source

SIFAT-SIFAT INTEGRAL RIEMANN-STIELTJES

Barekeng, 2007
If is limited and []ℜ→baf,:[]ℜ→ba,:α Monotone increase in [, is Riemann-Stieltjes integral able to α on ] ba,[]ba, simply written by[]αRSf∈ if . With JI=()()xdxfIbaα∫= is called Riemann Stieltjes lower integral f to α and ()()xdxfJbaα∫
Francis Y. Rumlawang, Harimanus Batkunde
doaj   +1 more source

SIFAT-SIFAT DASAR INTEGRAL HENSTOCK

Barekeng, 2012
This paper was a review about theory of Henstock integral. Riemann gave a definition of integral based on the sum of the partitions in Integration area (interval [a, b]). Those partitions is a  -positive constant.
Lexy J. Sinay
doaj   +1 more source

Inequalities for interval-valued Riemann diamond-alpha integrals

Journal of Inequalities and Applications, 2023
We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of ...
Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong   +3 more
doaj   +1 more source

Partially Explore the Differences and Similarities between Riemann-Liouville Integral and Mellin Transform

Fractal and Fractional, 2022
At present many researchers devote themselves to studying the relationship between continuous fractal functions and their fractional integral. But little attention is paid to the relationship between Mellin transform and fractional integral.
Zhibiao Zhou, Wei Xiao, Yongshun Liang
doaj   +1 more source