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17 results on '"41a55"'

1. Hermite–Hadamard-type inequalities for geometrically r-convex functions in terms of Stolarsky's mean with applications to means.

Author

Latif, Muhammad Amer

Subjects
*INTEGRAL inequalities, *CONVEX functions
Abstract

In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean inequality. [ABSTRACT FROM AUTHOR]

Published
2021
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2. Some k-fractional extensions of the trapezium inequalities through generalized relative semi-(m,h)-preinvexity.

Author

Du, Tingsong, Awan, Muhammad Uzair, Kashuri, Artion, and Zhao, Shasha

Subjects
*FRACTIONAL integrals, *EQUALITY, *MATHEMATICAL mappings
Abstract

In this paper, we first introduce the concept of generalized relative semi- (m , h) -preinvex functions, and then a new k-Riemann–Liouville fractional integral identity for differentiable mapping is derived. With the help of this identity, we present some new bounds on trapezium inequalities via generalized relative semi- (m , h) -preinvexity. It is pointed out that some new and known special cases can be deduced from main results of the article. [ABSTRACT FROM AUTHOR]

Published
2021
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3. Some parameterized inequalities by means of fractional integrals with exponential kernels and their applications.

Author

Zhou, Tai-Chun, Yuan, Zheng-Rong, Yang, Hong-Ying, and Du, Ting-Song

Subjects
*INTEGRAL inequalities, *FRACTIONAL integrals, *REAL numbers, *NUMERICAL analysis, *MATHEMATICAL equivalence, *DEFINITIONS, *MATHEMATICS, *GAUSSIAN quadrature formulas
Abstract

We use the definition of a new class of fractional integral operators, recently introduced by Ahmad et al. in [J. Comput. Appl. Math. 353:120–129, 2019], to establish a fractional-type integral identity with one parameter. We derive some parameterized integral inequalities for convex mappings based on this identity, and provide two examples to illustrate the investigated results as well. Moreover, we present applications of our findings to special means of real numbers, and error estimations for the quadrature formula in numerical analysis. [ABSTRACT FROM AUTHOR]

Published
2020
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4. Quantum Hermite–Hadamard inequality by means of a Green function.

Author

Adil Khan, Muhammad, Mohammad, Noor, Nwaeze, Eze R., and Chu, Yu-Ming

Subjects
*MATHEMATICAL equivalence, *IDENTITIES (Mathematics), *CONCAVE functions, *GREEN'S functions
Abstract

The purpose of this work is to present the quantum Hermite–Hadamard inequality through the Green function approach. While doing this, we deduce some novel quantum identities. Using these identities, we establish some new inequalities in this direction. We contemplate the possibility of expanding the method, outlined herein, to recast the proofs of some known inequalities in the literature. [ABSTRACT FROM AUTHOR]

Published
2020
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5. Some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions on co-ordinates.

Author

Xi, Bo-Yan, He, Chun-Ying, Qi, Feng, and Srivastava, Hari M.

Subjects
*CONVEX functions, *ANALYTIC geometry, *MATHEMATICAL inequalities, *HERMITE polynomials, *HADAMARD matrices
Abstract

In the paper, the authors introduce a new concept "extended ((s1, m1)-(s2, m2))-convex function on co-ordinates" and establish some new inequalities of the Hermite-Hadamard type for extended ((s1, m1)-(s2, m2))-convex functions of 2 variables on co-ordinates. [ABSTRACT FROM AUTHOR]

Published
2016
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6. Some Simpson type integral inequalities for functions whose third derivatives are (α, m)- GA-convex functions.

Author

Li, YuJiao and Du, TingSong

Abstract

By using power-mean integral inequality and Hölder’s integral inequality, this paper establishes some new inequalities of Simpson type for functions whose three derivatives in absolute value are the class of ( α ,  m )-geometric-arithmetically-convex functions. Finally, some applications to special means of positive real numbers have also been presented. [ABSTRACT FROM AUTHOR]

Published
2016
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7. Certain new bounds considering the weighted Simpson-like type inequality and applications

Author

Chunyan Luo, Mehmet Kunt, Tingsong Du, and Yao Zhang

Subjects
Pure mathematics, ( α , m , s ) $(\alpha,m,s)$ -convex function, media_common.quotation_subject, 010103 numerical & computational mathematics, 01 natural sciences, Discrete Mathematics and Combinatorics, Differentiable function, 26E60, 0101 mathematics, Simpson’s inequality, media_common, Mathematics, Applied Mathematics, Research, lcsh:Mathematics, 010102 general mathematics, Type inequality, lcsh:QA1-939, ( α , m , h ) $(\alpha,m,h)$ -convex function, 26D15, Identity (philosophy), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\alpha,m,s)$\end{document}(α,m,s)-convex function, 41A55, 26A33, Random variable, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\alpha,m,h)$\end{document}(α,m,h)-convex function, Analysis
Abstract

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables.

Published
2018
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13. Some new

Author

Nwaeze, Eze R., Kermausuor, Seth, and Tameru, Ana M.

Subjects
Hermite–Hadamard inequality, Strongly η-quasiconvex, 26D15, Research, Riemann–Liouville fractional integrals, 26A51, 41A55, 26E60
Abstract

A new class of quasiconvexity called strongly η-quasiconvex function was introduced in (Awan et al. in Filomat 31(18):5783–5790, 2017). In this paper, we obtain some new k-Riemann–Liouville fractional integral inequalities associated with this class of functions. For specific values of the associated parameters, we recover results due to Dragomir and Pearce (Bull. Aust. Math. Soc. 57:377–385, 1998), Ion (Ann. Univ. Craiova, Math. Sci. Ser. 34:82–87, 2007), and Alomari et al. (RGMIA Res. Rep. Collect. 12(Supplement):Article ID 14, 2009).

Published
2018

14. More results on Simpson’s type inequality through convexity for twice differentiable continuous mappings

Author

Sabir Hussain and Shahid Qaisar

Subjects
Pure mathematics, Strongly s-convex function, Multidisciplinary, Inequality, Computer science, Research, media_common.quotation_subject, 010102 general mathematics, Function (mathematics), Type (model theory), 01 natural sciences, Convexity, Integral identity, 010101 applied mathematics, Identity (mathematics), Holder’s integral inequality, 26D15, Statistics, 41A55, 26E60, Differentiable function, 0101 mathematics, Simpson’s inequality, media_common
Abstract

Our aim in this article is to incorporate the notion of “strongly s-convex function” and prove a new integral identity. Some new inequalities of Simpson type for strongly s-convex function utilizing integral identity and Holder’s inequality are considered.

Published
2016
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15. On some Hermite-Hadamard-type integral inequalities for co-ordinated $\boldsymbol{(\alpha, \mbox{QC})}$- and $\boldsymbol{(\alpha, \mbox{CJ})}$-convex functions

Author

Jian Sun, Bo-Yan Xi, and Shu-Ping Bai

Subjects
co-ordinated $(\alpha, \mbox{J})$-convex function, Pure mathematics, Hermite polynomials, Mathematical analysis, co-ordinated $(\alpha, \mbox{CJ})$-convex function, Type (model theory), co-ordinated $(\alpha, \mbox{QC})$-convex function, co-ordinated $(\alpha,\mbox{JQC})$-convex function, Hermite-Hadamard integral inequality, 26D15, Hadamard transform, 26A51, 41A55, 26E60, Convex conjugate, Convex function, 26D20, Geometry and topology, Mathematics
Abstract

In the article, the authors introduce the new concepts “co-ordinated $(\alpha, \mbox{QC})$-, $(\alpha,\mbox{JQC})$-, $(\alpha, \mbox{CJ})$- and $(\alpha, \mbox{J})$-convex functions”, establish some Hermite-Hadamard's type integral inequalities for the co-ordinated $(\alpha, \mbox{QC})$-, $(\alpha,\mbox{JQC})$-, $(\alpha, \mbox{CJ})$- and $(\alpha, \mbox{J})$-convex functions.

Published
2015
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16. On some Hermite-Hadamard type inequalities for (s, QC)-convex functions

Author

Feng Qi and Ying Wu

Subjects
Discrete mathematics, Mathematical optimization, Multidisciplinary, Hermite polynomials, Research, 010102 general mathematics, Mathematics::Classical Analysis and ODEs, Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing), Hermite–Hadamard’s integral inequality, Type (model theory), 01 natural sciences, 010101 applied mathematics, Mathematics::Logic, Convex function, 26D15, Hadamard transform, 26A51, 41A55, 26E60, 0101 mathematics, (s, QC)-Convex function on the co-ordinates, 26D20, Mathematics
Abstract

In the paper, the authors introduce a new notion “\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(s,\text {QC})$$\end{document}(s,QC)-convex function on the co-ordinates” and establish some Hermite–Hadamard type integral inequalities for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(s,\text {QC})$$\end{document}(s,QC)-convex functions on the co-ordinates.

Published
2015

17. Certain new bounds considering the weighted Simpson-like type inequality and applications.

Author

Luo, Chun-Yan, Du, Ting-Song, Kunt, Mehmet, and Zhang, Yao

Subjects
MATHEMATICAL equivalence, DIVERGENCE theorem, RANDOM variables, CONVEX functions, DIFFERENTIABLE mappings
Abstract

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables. [ABSTRACT FROM AUTHOR]

Published
2018
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