SOME LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED PREINVEX FUNCTIONS AND APPLICATIONS TO NUMERICAL QUADRATURE

被引：30

作者：

Sun, Wenbing ^{[1
]}

机构：

[1] Shaoyang Univ, Sch Sci, Shaoyang 422000, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2019年 / 27卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Generalized Preinvex Function; Generalized Preconcave Functions; Hermite- Hadamard Inequalities; Fractal Sets; Local Fractional Integral; HERMITE-HADAMARD TYPE; CONVEX-FUNCTIONS; SETS;

D O I：

10.1142/S0218348X19500713

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a new identity with parameters involving local fractional integrals is derived. Using this identity, some general local fractional integral inequalities for generalized preinvex functions are established. A parallel development is deduced for generalized preconcave functions. Taking special values for the parameters, some generalized midpoint inequalities, trapezoidal inequalities and Simpson inequalities are obtained. Finally, as some applications, error estimates of numerical integration for local fractional integrals are given.

引用

页数：14

共 31 条

[1] Local fractional integrals involving generalized strongly m-convex mappings [J].

Anastassiou, George ;

Kashuri, Artion ;

Liko, Rozana .

ARABIAN JOURNAL OF MATHEMATICS, 2019, 8 (02) :95-107

[2]

Awan MU, 2017, U POLITEH BUCH SER A, V79, P33

[3] Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex [J].

Barani, Ali ;

Ghazanfari, Amir G. ;

Dragomir, Sever S. .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,

[4] Properties and integral inequalities of Hadamard-Simpson type for the generalized (s,m)-preinvex functions [J].

Du, Ting-Song ;

Liao, Jia-Gen ;

Li, Yu-Jiao .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05) :3112-3126

[5] A generalization of Simpson's inequality via differentiable mapping using extended (s, m)-convex functions [J].

Du, Tingsong ;

Li, Yujiao ;

Yang, Zhiqiao .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 293 :358-369

[6] Generalized Pompeiu type inequalities for local fractional integrals and its applications [J].

Erden, Samet ;

Sarikaya, Mehmet Zeki .

APPLIED MATHEMATICS AND COMPUTATION, 2016, 274 :282-291

[7]

Iscan I, 2014, HACET J MATH STAT, V43, P935

[8]

Li Y., 2016, J. Egypt. Math. Soc, V24, P175, DOI [10.1016/j.joems.2015.05.009, DOI 10.1016/J.JOEMS.2015.05.009]

[9]

Mo H., 2014, ABSTR APPL ANAL

[10]

Mo Huixia, 2014, ABSTRACT AND APPLIED ANALYSIS, DOI [10.1155/2014/636751, DOI 10.1155/2014/636751]

← 1 2 3 4 →