Some Properties of Generalized Strongly Harmonic Convex Functions

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Muhammad Aslam Noor, Khalida Inayat Noor, Sabah Iftikhar, Farhat Safdar, Some Properties of Generalized Strongly Harmonic Convex Functions, Int. J. Anal. Appl., 16 (3) (2018), 427-436.

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Muhammad Aslam Noor, Khalida Inayat Noor, Sabah Iftikhar, Farhat Safdar

Abstract

In this paper, we introduce a new class of harmonic convex functions with respect to an arbitrary trifunction F( ·, ·, ·): K×K×[0,1]→R, which is called generalized strongly harmonic convex functions. We study some basic properties of strongly harmonic convex functions. We also discuss the sufficient conditions of optimality for unconstrained and inequality constrained programming under the generalized harmonic convexity. Several special cases are discussed as applications of our results. Ideas and techniques of this paper may motivate further research in different fields.

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References

  1. G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen, Generalized convexity and inequalities, J. Math. Anal. Appl., 335(2007), 1294-1308.
  2. M. S. Bazaraa, D. Hanif, C. M. Shetty, Nonlinear Programming Theory and Algorithms John Wiley and Sons, New York, 1993.
  3. C.R. Bector, C. Singh, B-vex functions, J. Optim. Theory Appl., 71 (1991), 439-453.
  4. M. T. Chao, J. B. Jian and D. Y. Liang, Sub-b-convex functions and sub-F-convex programming, Oper. Res. Trans., 16(2012), 1-8.
  5. I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions. Hacet, J. Math. Stats., 43(6)(2014), 935-942.
  6. J. Liao and T. Du, On some characterizations of sub-b-s-convex functions, Filomat, 30(14)(2016), 3885-3895.
  7. C. P. Niculescu and L. E. Persson, Convex Functions and Their Applications, Springer-Verlag, New York, (2006).
  8. M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput. 251(2004), 199-277.
  9. M. A. Noor and K. I. Noor, Harmonic variational inequalities, Appl. Math. Inf. Sci., 10(5)(2016), 1811-1814.
  10. M. A. Noor and K. I. Noor, Some implicit methods frsolving harmonic variational inequalites, Inter. J. Anal. Appl. 12(1)(2016), 10-14.
  11. M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for strongly harmonic convex functions, J. Inequ. Special Func.,7(3)(2016), 99-113.
  12. M. A. Noor, K. I. Noor and S. Iftikhar, Integral inequalities for differentiable relative harmonic preinvex functions(survey), TWMS J. Pure Appl. Math. 7(1)(2016), 3-19.
  13. M. A. Noor, K. I. Noor and S. Iftikhar, Hermite-Hadamard inequalities for harmonic preinvex functions, Saussurea 6(1)(2016), 34-53.
  14. M. A. Noor, K. I. Noor and S. Iftikhar, Integral inequalities of Hermite-Hadamard type for harmonic (h,s)-convex functions, Int. J. Anal. Appl., 11(1)(2016), 61-69.
  15. M. A. Noor, K. I. Noor, S. Iftikhar and F. Safdar, Integral inequalities for relative harmonic (s,η)-convex functions, Appl. Math. Comput. Sci. 1(1)(2016), 27-34.
  16. M. A. Noor, K. I. Noor, S. Iftikhar and C. Ionescu, Hermite-Hadamard inequalities for co-ordinated harmonic convex functions, U.P.B. Sci. Bull., Ser: A, 79(1)(2017), 25-34.
  17. M. A. Noor, K. I. Noor and S. Iftikhar, Some characterizations of harmonic convex functions, Int. J. Anal. Appl. 15(2)(2017), 179-187.
  18. M. A. Noor, B. Bin-Mohsin, K. I. Noor and S. Iftikhar, Relative strongly harmonic convex functions and their characteri- zations, J. Nonlinear Sci. Appl. in press.
  19. J. Pecaric, F. Proschan, and Y. L. Tong, Convex Functions, Partial Orderings and Statistical Applications, Acdemic Press, New York, (1992).
  20. T.-Y. Zhang, Ai-P. Ji, F. Qi, Integral inequalities of Hermite-Hadamard type for harmonically quasi-convex functions, Proc. Jangjeon. Math. Soc., 16(3)(2013), 399-407.