호남수학학술지 (Honam Mathematical Journal)

  • 제40권2호
  • /
  • Pages.239-250
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  • 2018
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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NEWTON INEQUALITIES FOR p-HARMONIC CONVEX FUNCTIONS

  • 투고 : 2017.12.04
  • 심사 : 2018.03.07
  • 발행 : 2018.06.25
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초록

In this paper, we establish some new Newton's type integral inequalities for p-harmonic convex functions. Some special cases are also discussed as applications of our main results. Results obtained in this paper may be starting point for further research.

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참고문헌

  1. G. D. Anderson. M. K. Vamanamurthy and M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl, 335 (2007), 1294-1308. https://doi.org/10.1016/j.jmaa.2007.02.016
  2. G. Cristescu and L. Lupsa, Non-connected Convexities and Applications, Kuler Academic Publisher, Dordrecht, Holland, 2002.
  3. S. Gao and W. Shi, On new ineaulities of Newton's type for functions whose secong derivatives absolute values are convex, Int. J. Pure Appl. Math. 74(1) (2012), 33-41.
  4. C. Hermite, Sur deux limites d'une intgrale dfinie, Mathesis. 3 (1883), Art. 82.
  5. J. Hadamard, Etude sur les proprietes des fonctions entieres e.t en particulier dune fonction consideree par Riemann. J. Math. Pure Appl. 58 (1893), 171-215.
  6. I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe, J. Math. Stat. 43(6) (2014), 935-942.
  7. I. Iscan, Hermite-Hadamard and Simpson like inequalities for differentiable harmonically convex functions, J. Math. 10 (2014), Article ID 346305.
  8. M. V. Mihai, M. A. Noor, K. I. Noor and M. U. Awan, Some integral inequalities for harmonic h-convex functions involving hypergeometric functions, Appl. Math. Comput. 252 (2015), 257-262.
  9. M. A. Noor, Advance Convex Analysis, Lecture Notes, Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2008-2017.
  10. M. A. Noor, K. I. Noor and M. U. Awan, Some Newton's type inequalities for geometrically relative convex functions, Malaysian J. Math. Sci. 9(3) (2015), 491-502.
  11. M. A. Noor, K. I. Noor and M. U. Awan, Some integral inequalities for harmonivally h-convex functions, U.P.B. Sci. Bull, Ser. A, Appl. Math. Phy. 77(1) (2015), 5-16.
  12. M. A. Noor, K. I. Noor and S. Iftikhar, Some Newton's type inequalities for harmonic convex functions, J. Adv. Math. Stud. 9(1) (2016), 07-16.
  13. M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalites for harmonic nonconvex functions, MAGNT Research Report, 4(1) (2016), 24-40.
  14. M. A. Noor, K. I. Noor and S. Iftikhar, Integral inequalities for differentiable p-harmonic convex functions, Filomat, 31(20) (2017), 6575-6584. https://doi.org/10.2298/FIL1720575N
  15. M. A. Noor, K. I. Noor and S. Iftikhar, Inequalities via strongly p-harmonic log-convex functions, J. Nonl. Funct. Anal. 2017 (2017), Article ID 20.
  16. C. P. Niculescu and L. E. Persson, Convex Functions and Their Applications, Springer-Verlag, New York, 2006.
  17. J. E. Pecaric, J. H. Proschan and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Acdemic Press, London, 1992.
  18. H. N. Shi and J. Zhang, Some new judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions, J. Inequal. Appl. 2013 (2013): 527. https://doi.org/10.1186/1029-242X-2013-527
  19. K. S. Zhang and J. P. Wan, p-convex functions and their properties, Pure Appl. Math. 23(1)(2007), 130-133.