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Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration Cover

Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration

By: S. Erden,  M. Z. Sarikaya and  N. Çelik  
Open Access
|Dec 2016

References

  1. [1] A. Akkurt, M.Z. Sarıkaya, H. Budak and H. Yıldırım, Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals, RGMIA Research Report Collection, 18(2015), Article 171, 11 pp.
  2. [2] N. S. Barnett, S.S. Dragomir and R. P. Agarwal, Some inequalities for probability, expectation, and variance of random variables defined over a finite interval, Computer and Math. with Appl., 43 (2002), 1319-1357.10.1016/S0898-1221(02)00103-7
  3. [3] P. Cerone and S.S. Dragomir, Three Point Quadrature Rules Involving, at Most, a First Derivative, RGMIA Res. Rep. Coll., 4,2(1999), Article 8.
  4. [4] G-S. Chen, Generalizations of Hölder’s and some related integral inequalities on fractal space, Journal of Function Spaces and Applications Volume 2013, Article ID 198405.10.1155/2013/198405
  5. [5] S. S. Dragomir and I. Fedotov, An inequality of Grüss type for Riemann-Stieltjes integral and applications for special means, Tamkang J. of Math., 29(4), 287-292, 1998.10.5556/j.tkjm.29.1998.4257
  6. [6] S.S. Dragomir, Some integral inequalities of Grüss type, Indian J. Pure Appl. Math., 31(4), 397-415, 2000.10.1155/S1025583400000084
  7. [7] S.S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and for some numerical quadrature rules, Applied Mathematics Letters, 11(1), 105-109, 1988.10.1016/S0893-9659(97)00142-0
  8. [8] S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüss’ type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic. Vol. 33, No. 11, pp. 15-20, 1997.10.1016/S0898-1221(97)00084-9
  9. [9] Erden S, and Sarikaya MZ. Generalized Pompeiu type inequalities for local fractional integrals and Its Applications, Applied Math. and Computations, 274 (2016) 282-291.
  10. [10] G. Grüss, Über das maximum des absoluten Betrages von1baabf(x)g(x)dx1(ba)2abf(x)dxabg(x)dx${1 \over {b - a}}\int\limits_a^b {f(x)g(x)dx - {1 \over {\left( {b - a} \right)^2 }}\int\limits_a^b {f(x)dx\int\limits_a^b {g(x)dx} } }$, Math. Z., 39, 215-226, 1935.10.1007/BF01201355
  11. [11] D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1991.10.1007/978-94-011-3562-7_15
  12. [12] M. Matić, J.E. Pečarić and N. Ujević, On new estimation of the remainder in generalized Taylor’s formula, Math. Ineq. & Appl., 3,2(1999), 343-361.10.7153/mia-02-31
  13. [13] H. Mo, X Sui and D Yu, Generalized convex functions on fractal sets and two related inequalities, Abstract and Applied Analysis, Volume 2014, Article ID 636751, 7 pages.10.1155/2014/636751
  14. [14] A. M. Ostrowski, Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert, Comment. Math. Helv. 10(1938), 226-227.10.1007/BF01214290
  15. [15] B. G. Pachpatte, On Čebyšev-Grüss type inequalities via Pecaric’s extention of the Montgomery identity, J. Inequal. Pure and Appl. Math. 7(1), Art 108, 2006.
  16. [16] Sarikaya, M. Z., A Note on Grüss type inequalities on time scales, Dynamic Systems and Applications, 17 (2008), 663-666.
  17. [17] M. Z. Sarikaya and H Budak, Generalized Ostrowski type inequalities for local fractional integrals, RGMIA Research Report Collection, 18(2015), Article 62, 11 pp.
  18. [18] M. Z. Sarikaya, S. Erden and H. Budak, Some generalized Ostrowski type inequalities involving local fractional integrals and applications, RGMIA Research Report Collection, 18(2015), Article 63, 12 pp.
  19. [19] M. Z. Sarikaya, T. Tunc and H. Budak, On generalized some integral inequalities for local fractional integrals, RGMIA Research Report Collection, 18(2015), Article 87, 13 pp.
  20. [20] X. J. Yang, Advanced Local Fractional Calculus and Its Applications, World Science Publisher, New York, 2012.
  21. [21] J. Yang, D. Baleanu and X. J. Yang, Analysis of fractal wave equations by local fractional Fourier series method, Adv. Math. Phys., 2013 (2013), Article ID 632309.10.1155/2013/632309
  22. [22] X. J. Yang, Local fractional integral equations and their applications, Advances in Computer Science and its Applications (ACSA) 1(4), 2012.
  23. [23] X. J. Yang, Generalized local fractional Taylor’s formula with local fractional derivative, Journal of Expert Systems, 1(1) (2012) 26-30.
  24. [24] X. J. Yang, Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications 1(1), 2012 12-16.
DOI: https://doi.org/10.1515/jamsi-2016-0008 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 49 - 65
Published on: Dec 30, 2016
Published by: University of Ss. Cyril and Methodius in Trnava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2016 S. Erden, M. Z. Sarikaya, N. Çelik, published by University of Ss. Cyril and Methodius in Trnava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.