Hermite-Hadamard and Hermite-Hadamard-Fejer Type Inequalities Involving Fractional Integral Operators

被引:8
作者
Set, Erhan [1 ]
Akdemir, Ahmet Ocak [2 ]
Alan, Emrullah Aykan [1 ]
机构
[1] Ordu Univ, Fac Sci & Arts, Dept Math, Ordu, Turkey
[2] Ibrahim Cecen Univ Agri, Fac Arts & Sci, Dept Math, Agri, Turkey
关键词
Convex function; Quasi-convex function; Symmetrized convex function; Wright-quasi-convex functions; Hermite-Hadamard type inequalities; Generalized fractional integral operators; Hermite-Hadamard-Fejer type inequalities; CONVEX-FUNCTIONS;
D O I
10.2298/FIL1908367S
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Since the so-called Hermite-Hadamard type inequalities for convex functions were presented, their generalizations, refinements, and variants involving various integral operators have been extensively investigated. Here we aim to establish several Hermite-Hadamard inequalities and Hermite-Hadamard-Fejer type inequalities for symmetrized convex functions and Wright-quasi-convex functions with a weighted function symmetric with respect to the midpoint axis on the interval involving the fractional conformable integral operators initiated by Jarad et al. [9]. We also point out that certain known inequalities are particular cases of the results presented here.
引用
收藏
页码:2367 / 2380
页数:14
相关论文
共 12 条
[1]   Properties of h-convex functions related to the Hermite-Hadamard-Fejer inequalities [J].
Bombardelli, Mea ;
Varosanec, Sanja .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (09) :1869-1877
[2]  
Dragomir S., 2000, Selected Topics on Hermite-Hadamard Inequalities and Applications
[3]   SYMMETRIZED CONVEXITY AND HERMITE-HADAMARD TYPE INEQUALITIES [J].
Dragomir, S. S. .
JOURNAL OF MATHEMATICAL INEQUALITIES, 2016, 10 (04) :901-918
[4]  
Dragomir S. S., 2017, RGMIA RES REP COLL, V20
[5]   Quasi-convex functions and Hadamard's inequality [J].
Dragomir, SS ;
Pearce, CEM .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1998, 57 (03) :377-385
[6]  
El Farissi A, 2012, REAL ANAL EXCH, V38, P467
[7]  
Fejr L., 1906, Anz Ungar. Akad. Wiss., V24, P369
[8]  
Iscan I, 2015, STUD U BABES-BOL MAT, V60, P355
[9]   On a new class of fractional operators [J].
Jarad, Fahd ;
Ugurlu, Ekin ;
Abdeljawad, Thabet ;
Baleanu, Dumitru .
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[10]  
Mitrinovic M. S., 1985, Aequationes Math., V28, P229, DOI [DOI 10.1007/BF02189414, 10.1007/BF02189414]