New generalized fractional versions of Hadamard and Fejer inequalities for harmonically convex functions

被引：16

作者：

Qiang, Xiaoli ^{[1
]}

Farid, Ghulam ^{[2
]}

Yussouf, Muhammad ^{[3
]}

Khan, Khuram Ali ^{[3
]}

Rahman, Atiq Ur ^{[2
]}

机构：

[1] Guangzhou Univ, Inst Comp Sci & Technol, Guangzhou 510006, Peoples R China

[2] COMSATS Univ Islamabad, Dept Math, Attock Campus, Attock, Pakistan

[3] Univ Sargodha, Dept Math, Sargodha, Pakistan

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2020年 / 2020卷 / 01期

关键词：

Harmonically convex function; Hadamard inequality; Fejer-Hadamard inequality; Mittag-Leffler function; Fractional integral operators; MITTAG-LEFFLER FUNCTION; HERMITE-HADAMARD; INTEGRAL-INEQUALITIES; STABILITY; EXISTENCE;

D O I：

10.1186/s13660-020-02457-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to establish new generalized fractional versions of the Hadamard and the Fejer-Hadamard integral inequalities for harmonically convex functions. Fractional integral operators involving an extended generalized Mittag-Leffler function which are further generalized via a monotone increasing function are utilized to get these generalized fractional versions. The results of this paper give several consequent fractional inequalities for harmonically convex functions for known fractional integral operators deducible from utilized generalized fractional integral operators.

引用

页数：13

共 44 条

[1] A FURTHER EXTENSION OF MITTAG-LEFFLER FUNCTION [J].

Andric, Maja ;

Farid, Ghulam ;

Pecaric, Josip .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (05) :1377-1395

[2]

[Anonymous], 2017, J ANAL-INDIA, DOI DOI 10.1007/S41478-017-0032-Y

[3]

CHEN F, 2014, J APPL MATH, V2014

[4] Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals [J].

Chen, Hua ;

Katugampola, Udita N. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 446 (02) :1274-1291

[5] ON MINKOWSKI AND HERMITE-HADAMARD INTEGRAL INEQUALITIES VIA FRACTIONAL INTEGRATION [J].

Dahmani, Zoubir .

ANNALS OF FUNCTIONAL ANALYSIS, 2010, 1 (01) :51-58

[6]

Ekinci A, 2019, APPL COMPUT MATH-BAK, V18, P288

[7]

Farid G., 2016, NONLINEAR ANAL FORUM, V21, P77

[8]

Farid G., 2018, J MATH COMPUT SCI, V8, P630

[9]

Farid G., 2020, OPEN J MATH ANAL, V4, P1, DOI [10.30538/psrp-oma2020.0047, DOI 10.30538/PSRP-OMA2020.0047]

[10] HADAMARD AND FEJER-HADAMARD TYPE INEQUALITIES FOR CONVEX AND RELATIVE CONVEX FUNCTIONS VIA AN EXTENDED GENERALIZED MITTAG-LEFFLER FUNCTION [J].

Farid, Ghulam ;

Mishra, Vishnu Narayan ;

Mehmood, Sajid .

INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2019, 17 (05) :892-903

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