FRACTIONAL TYPE HERMITE-HADAMARD INEQUALITIES FOR CONVEX AND AG(Log)-CONVEX FUNCTIONS ∗

In this paper, we give a new type integral equality involving left-sided and right-sided Riemann-Liouville fractional integrals. Thereafter, some new fractional type Hermite-Hadamard inequalities are presented by using the above fractional integral equality involving the concepts of convex functions and $s$-convex functions and AG(log)-convex functions respectively.

[1]  Vishnu Narayan Mishra,et al.  Degree of Approximation of Functions f ∈ Hω Class by the (Np E1) Means in the Hölder Metric , 2014, Int. J. Math. Math. Sci..

[2]  Deepmala,et al.  Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators , 2013, SSRN Electronic Journal.

[3]  Deepmala,et al.  A Study on Some Problems on Existence of Solutions for Nonlinear Functional-Integral Equations , 2013 .

[4]  Michal Feckan,et al.  Hermite–Hadamard-type inequalities for r-convex functions based on the use of Riemann–Liouville fractional integrals , 2013, Ukrainian Mathematical Journal.

[5]  Deepmala,et al.  Study on existence of solutions for some nonlinear functional-integral equations with applications , 2013 .

[6]  Mehmet Zeki Sarikaya,et al.  Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities , 2013, Math. Comput. Model..

[7]  Kuei-Lin Tseng,et al.  Hadamard-type and Bullen-type inequalities for Lipschitzian functions and their applications , 2012, Comput. Math. Appl..

[8]  S. Dragomir.  Hermite–Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces , 2012 .

[9]  Constantin P. Niculescu.  The Hermite–Hadamard inequality for log-convex functions , 2012, Nonlinear Analysis: Theory, Methods & Applications.

[10]  M. Emin Özdemir,et al.  Hermite-Hadamard-type inequalities via (α, m)-convexity , 2011, Comput. Math. Appl..

[11]  M. Özdemir,et al.  New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications , 2011, Appl. Math. Comput..

[12]  Mihály Bessenyei,et al.  The Hermite–Hadamard inequality in Beckenbach's setting☆ , 2010 .

[13]  J. Cárcamo,et al.  A general multidimensional Hermite―Hadamard type inequality , 2009 .

[14]  Shyam Lal,et al.  Approximation of functions belonging to the generalized Lipschitz Class by C1 * Np summability method of fourier series , 2009, Appl. Math. Comput..

[15]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[16]  Lech Maligranda,et al.  Some remarks ons-convex functions , 1994 .

[17]  Feng Qi (祁锋),et al.  Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals of (α,m)-convex functions , 2014 .

[18]  Feng Qi (祁锋),et al.  Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions , 2013 .

[19]  Jinrong Wang,et al.  Hermite-Hadamard Type Inequalities for r-Convex Functions via Riemann-Liouville Fractional Integrals , 2013 .

[20]  Constantin P. Niculescu.  Convexity according to the geometric mean , 2000 .