Title: Some Integral Inequalities for Local Fractional Integrals
Author(s): M. Zeki Sarikaya, samet Erden, Hüseyin Budak
Pages: 9-19
Cite as:
M. Zeki Sarikaya, samet Erden, Hüseyin Budak, Some Integral Inequalities for Local Fractional Integrals, Int. J. Anal. Appl., 14 (1) (2017), 9-19.

Abstract


In this paper, firstly we extend some generalization of the Hermite-Hadamard inequality and Bullen inequality to generalized convex functions. Then, we give some important integral inequalities related to these inequalities.

Full Text: PDF

 

References


  1. P. S. Bullen, Error estimates for some elementary quadrature rules, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (1978) 602-633, (1979) 97-103.

  2. S. S. Dragomir and R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5) (1998), 91-95.

  3. S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

  4. S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (5) (1998), 91-95.

  5. A. El Farissi, Z. Latreuch and B. Belaidi, Hadamard-Type inequalities for twice diffrentiable functions, RGMIA Research Report Collection, 12 (1) (2009), Art. ID 6.

  6. A. El Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal. 4 (3) (2010), 365-369.

  7. X. Gao, A note on the Hermite-Hadamard inequality, JMI Jour. Math. Ineq..4 (4) (2010), 587-591.

  8. J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction consideree par Riemann, J. Math. Pures Appl. 58 (1893), 171-215.

  9. U. S. Kirmaci and M. E. Ozdemir, On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math Comput. 153 (2004), 361–368.

  10. U. S. Kirmaci and R. Dikici, On some Hermite-Hadamard type inequalities for twice differentiable mappings and applications, Tamkang J. Math. 44 (1) (2013), 41–51.

  11. U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (2004) 137–146.

  12. D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and new inequalities in analysis, ser. Math. Appl. (East European Ser.). Dordrecht: Kluwer Academic Publishers Group, vol. 61, 1993.

  13. H. Mo, X. Sui and D. Yu, Generalized convex functions on fractal sets and two related inequalities, Abstr. Appl. Anal. 2014 (2014), Art. ID 636751, 7 pages.

  14. M. Z. Sarikaya and H. Yaldiz, On the Hadamard’s type inequalities for L-Lipschitzian mapping, Konuralp J. Math. 1 (2) (2013), 33-40.

  15. X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, 2012.

  16. J. Yang, D. Baleanu and X. J. Yang, Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys. 2013 (2013), Art. ID 632309.