Results 1 to 10 of about 360,754 (261)
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 +3 more
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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
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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 +3 more
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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
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On new Milne-type inequalities and applications
Journal of Inequalities and Applications, 2023 Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland’s integral for the stellar absorption.
Paul Bosch +2 more
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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
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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 +3 more
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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
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Hermite-Jensen-Mercer type inequalities via Ψ-Riemann-Liouville k-fractional integrals
AIMS Mathematics, 2020 Integral inequalities involving various fractional integral operators are used to solve many fractional differential equations. In this paper, authors prove some Hermite-Jensen-Mercer type inequalities using Ψ-Riemann-Liouville k-Fractional integrals via
Saad Ihsan Butt +4 more
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A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators
Axioms, 2023 A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented.
Muhammad Tariq +2 more
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