Bounds Involving Operator s-Godunova-Levin-Dragomir Functions

  • Muhammad Aslam Noor
  • Muhammad Uzair Awan
  • Khalida Inayat Noor
Part of the Springer Optimization and Its Applications book series (SOIA, volume 131)


The objective of this chapter is to introduce a new class of operator s-Godunova-Levin-Dragomir convex functions. We also derive some new Hermite-Hadamard-like inequalities for operator s-Godunova-Levin-Dragomir convex functions of positive operators in Hilbert spaces.



Authors would like to express their gratitude to Prof. Dr. Themistocles M. Rassias for his kind invitation. Authors are pleased to acknowledge the “support of Distinguished Scientist Fellowship Program(DSFP), King Saud University,” Riyadh, Saudi Arabia.


  1. 1.
    Bacak, V., Turkmen, R.: New inequalities for operator convex functions. J. Inequal. Appl. 2013, 190 (2013)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Breckner, W.W.: Stetigkeitsaussagen ir eine Klasse verallgemeinerter convexer funktionen in topologischen linearen Raumen. Pupl. Inst. Math. 23, 13–20 (1978)Google Scholar
  3. 3.
    Cristescu, G., Lupsa, L.: Non-connected Convexities and Applications. Kluwer Academic Publishers, Dordrecht (2002)CrossRefGoogle Scholar
  4. 4.
    Dragomir, S.S.: The Hermite-Hadamard type inequalities for operator convex functions. Appl. Math. Comput. 218(3), 766–772 (2011). MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dragomir, S.S.: Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces (2014, preprint)Google Scholar
  6. 6.
    Dragomir, S.S., Fitzpatrick, S.: The Hadamard’s inequality for s-convex functions in the second sense. Demonstratio Math. 32(4), 687–696 (1999)Google Scholar
  7. 7.
    Dragomir, S.S., Pearce, C.E.M.: Selected Topics on Hermite-Hadamard Inequalities and Applications. (RGMIA Monographs, Victoria University (2000)
  8. 8.
    Furuta, T., Micic Hot, J., Pecaric, J., Seo, Y.: Mond-Pecaric Method in Operator Inequalities, Inequalities for Bounded Selfadjoint Operators on a Hilbert Space. Element, Zagreb (2005)Google Scholar
  9. 9.
    Ghazanfari, A.G.: The Hermite-Hadamard type inequalities for operator s-convex functions. J. Adv. Res. Pure Math. 6(3), 52–61 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ghazanfari, A.G., Shakoori, M., Barani, A., Dragomir, S.S.: Hermite-Hadamard type inequality for operator preinvex functions, arXiv:1306.0730v1 [math.FA] 4 Jun 2013Google Scholar
  11. 11.
    Mond, B., Pecaric, J.: On some operator inequalities. Indian J. Math. 35, 221–232 (1993)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Noor, M.A., Noor, K.I., Awan, M.U.: Fractional Ostrowski inequalities for s-Godunova-Levin functions. Int. J. Anal. Appl. 5, 167–173 (2014)zbMATHGoogle Scholar
  13. 13.
    Noor, M.A., Noor, K.I., Awan, M.U., Khan, S.: Fractional Hermite-Hadamard inequalities for some new classes of Godunova-Levin functions. Appl. Math. Inf. Sci. 8(6), 2865–2872 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Pachpatte, B.G.: On some inequalities for convex functions. RGMIA Research Report Collection 6(E) (2003)Google Scholar
  15. 15.
    Pecaric, J.E., Proschan, F., Tong, Y.L.: Convex Functions, Partial Orderings, and Statistical Applications. Academic, San Diego (1992)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Muhammad Aslam Noor
    • 1
    • 2
  • Muhammad Uzair Awan
    • 3
  • Khalida Inayat Noor
    • 4
  1. 1.Mathematics DepartmentKing Saud UniversityRiyadhSaudi Arabia
  2. 2.COMSATS Institute of Information TechnologyIslamabadPakistan
  3. 3.GC UniversityFaisalabadPakistan
  4. 4.COMSATS Institute of Information TechnologyIslamabadPakistan

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