Riemann-Liouville fractional Hermite-Hadamard inequalities. Part II: for twice differentiable geometric-arithmetically s-convex functions
نویسندگان
چکیده
*Correspondence: [email protected]; [email protected] 1School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, P.R. China 2Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China Full list of author information is available at the end of the article Abstract Motivated by the definition of geometric-arithmetically s-convex functions in (Shuang et al. in Analysis 33:197-208, 2013) and second-order fractional integral identities in (Zhang and Wang in J. Inequal. Appl. 2013:220, 2013; Wang et al. in Appl. Anal. 2012, doi:10.1080/00036811.2012.727986), we establish some interesting Riemann-Liouville fractional Hermite-Hadamard inequalities for twice differentiable geometric-arithmetically s-convex functions via beta function and incomplete beta function. MSC: 26A33; 26A51; 26D15
منابع مشابه
Fractional Hermite-Hadamard type inequalities for n-times log-convex functions
In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.
متن کاملSOME GENERALIZED HERMITE-HADAMARD TYPE INEQUALITIES INVOLVING FRACTIONAL INTEGRAL OPERATOR FOR FUNCTIONS WHOSE SECOND DERIVATIVES IN ABSOLUTE VALUE ARE s-CONVEX
In this article, a general integral identity for twice differentiable mapping involving fractional integral operators is derived. As a second, by using this identity we obtained some new generalized Hermite-Hadamards type inequalities for functions whose absolute values of second derivatives are s-convex and concave. The main results generalize the existing Hermite-Hadamard type inequalities in...
متن کاملA generalized form of the Hermite-Hadamard-Fejer type inequalities involving fractional integral for co-ordinated convex functions
Recently, a general class of the Hermit--Hadamard-Fejer inequality on convex functions is studied in [H. Budak, March 2019, 74:29, textit{Results in Mathematics}]. In this paper, we establish a generalization of Hermit--Hadamard--Fejer inequality for fractional integral based on co-ordinated convex functions.Our results generalize and improve several inequalities obtained in earlier studies.
متن کاملSome extended Simpson-type inequalities and applications
In this paper, we shall establish some extended Simpson-type inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Simpson formula are also given.
متن کاملGeneralized Hermite-Hadamard type inequalities involving fractional integral operators
In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liou...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013