Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity

References

• Mitrinović , DS and Lacković , IB . 1985 . Hermite and convexity . Aequat. Math. , 28 : 229 – 232 .
   Google Scholar
• Dragomir , SS . 1992 . On Hadamard's inequalities for convex functions . Math. Balkanica , 6 : 215 – 222 .
   Google Scholar
• Dragomir , SS and McAndrew , A . 2005 . Refinements of the Hermite–Hadamard inequality for convex functions . J. Inequal. Pure Appl. Math. , 6 : 1 – 6 . Article 140
   Web of Science ®Google Scholar
• Merentesm , N and Nikodem , K . 2010 . Remarks on strongly convex functions . Aequat. Math. , 80 : 193 – 199 .
   Web of Science ®Google Scholar
• Toader , GH . 1984 . Some generalizations of the convexity . Proc. Colloq. Approx. Optim. , : 329 – 338 .
   Google Scholar
• Bakula , MK , Ödemir , ME and Pe[cbreve]rić , J . 2008 . Hadamard type inequalities for m-convex and (α, m)-convex functions . J. Inequal. Pure Appl. Math. , 9 : 1 – 9 . Article 96
   Google Scholar
• Pinheiro , MR . 2007 . Exploring the concept of s-convexity . Aequat. Math. , 74 : 201 – 209 .
   Google Scholar
• Bakula , MK , Pe[cbreve]rić , J and Ribi[cbreve]ić , M . 2006 . Companion inequalities to Jensen's inequality for m-convex and (α, m)-convex functions . J. Inequal. Pure Appl. Math. , 7 : 1 – 7 . Article 194
   Web of Science ®Google Scholar
• Ödemir , ME , Avci , M and Set , E . 2010 . On some inequalities of Hermite–Hadamard-type via m-convexity . Appl. Math. Lett. , 23 : 1065 – 1070 .
   Web of Science ®Google Scholar
• Ödemir , ME , Avci , M and Kavurmaci , H . 2011 . Hermite–Hadamard-type inequalities via (α, m)-convexity . Comput. Math. Appl. , 61 : 2614 – 2620 .
   Web of Science ®Google Scholar
• Özdemir , ME , Kavurmaci , H and Set , E . 2010 . Ostrowski's type inequalities for (α, m)-convex functions . Kyungpook Math. J. , 50 : 371 – 378 .
   Google Scholar
• Ödemir , ME , Set , E and Sarikaya , MZ . 2011 . Some new Hadamard's type inequalities for co-ordinated m-convex and (α, m)-convex functions . Hacettepe J. Math. Stat. , 40 : 219 – 229 .
   Web of Science ®Google Scholar
• Set , E , Sardari , M , Ozdemir , ME and Rooin , J . 2009 . On generalizations of the Hadamard inequality for (α, m)-convex functions . RGMIA Res. Rep. Coll. , 12 : 1 – 10 . Article 4
   Google Scholar
• Xi , B , Bai , R and Qi , F . 2012 . Hermite–Hadamard-type inequalities for the m-and (α, m)-geometrically convex functions . Aequat. Math. , Online, doi:10.1007/s00010-011-0114-x
   Web of Science ®Google Scholar
• Sarikaya , MZ , Set , E , Yaldiz , H and Başak , N . 2012 . Hermite–Hadamard's inequalities for fractional integrals and related fractional inequalities . Math. Comput. Model. , Online, doi:10.1016/j.mcm.2011.12.048
   Web of Science ®Google Scholar
• Baleanu , D , Machado , JAT and Luo , AC-J . 2012 . Fractional Dynamics and Control , New York : Springer .
   Google Scholar
• Diethelm , K . 2010 . The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics , Berlin : Springer .
   Google Scholar
• Kilbas , AA , Srivastava , HM and Trujillo , JJ . 2006 . Theory and Applications of Fractional Differential Equations , Amsterdam : Elsevier Science B.V. .
   Google Scholar
• Lakshmikantham , V , Leela , S and Devi , JV . 2009 . Theory of Fractional Dynamic Systems , Cambridge : Cambridge Scientific Publishers .
   Google Scholar
• Miller , KS and Ross , B . 1993 . An Introduction to the Fractional Calculus and Differential Equations , New York : John Wiley .
   Google Scholar
• M.W. Michalski, Derivatives of noninteger order and their applications, Diss. Mathematicae, CCCXXVIII, Institute of Mathematics, Polish Academy of Sciences, 1993
   Google Scholar
• Podlubny , I . 1999 . Fractional Differential Equations , San Diego : Academic Press .
   Google Scholar
• Tarasov , VE . 2011 . Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media , Heidelberg, HEP : Springer .
   Google Scholar