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New Inequalities for Preinvex Functions

Year 2019, Volume: 7 Issue: 1, 54 - 61, 30.04.2019

Huriye Kadakal İmdat İşcan

https://doi.org/10.36753/mathenot.559247

Abstract

In this study, a new identity for functions defined on an open invex subset of set of real numbers is
formed. After that we established Hermite-Hadamard-like inequalities for this type of functions. Then, by
using the this identity and the Hölder and Power mean integral inequalities we present new type integral
inequalities for functions whose powers of fourth derivatives in absolute value are preinvex functions.

Keywords

Invex set preinvex function Hölder Integral inequality

References

  • [1] Barani, A., Ghazanfari AG, Dragomir SS. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex. Journal of Inequalities and Applications. 2012 (2012):247.
  • [2] Dragomir, SS. and Pearce, CEM., Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University, 2000.
  • [3] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par Riemann. J. Math. Pures Appl. 58 (1893), 171-215.
  • [4] Israel, AB. and Mond, B., What is invexity? J. Aust. Math. Soc.Ser. B. 28 (1986), 1-9.
  • [5] ˙I¸scan, ˙I., Set, E. and Özdemir, ME., On new general integral inequalities for s-convex functions. Applied Mathematics and Computation. 246 (2014), 306-315.
  • [6] ˙I¸scan ˙I., Ostrowski type inequalities for functions whose derivatives are preinvex. Bulletin of the Iranian Mathematical Society. 40 (2014), 2, 373-386.
  • [7] Latif, MA. and Dragomir, SS., Some Hermite-Hadamard type inequalities for functions whose partial derivatives in absloute value are preinvex on the co-oordinates. Facta Universitatis (NIŠ) Ser. Math. Inform. 28 (2013), No. 3, 257-270.
  • [8] Maden, S., Kadakal, H., Kadakal, M. and ˙I ¸scan ˙I., Some new integral inequalities for n-times differentiable convex functions. J. Nonlinear Sci. Appl. 10 (2017), 12, 6141-6148.
  • [9] Matloka, M., On some new inequalities for differentiable (h1; h2)-preinvex functions on the co-ordinates. Mathematics and Statistics. 2 (2014), 1, 6-14.
  • [10] Mohan, SR., Neogy, SK., On invex sets and preinvex functions. J. Math. Anal. Appl. 189 (1995), 901-908.
  • [11] Noor, MA., Hermite-Hadamard integral inequalities for log-preinvex functions. J. Math. Anal. Approx. Theory. 2 (2007), 126-131.
  • [12] Noor, MA., Invex equilibrium problems. J. Math. Anal. Appl. 302 (2005), 463-475.
  • [13] Noor, MA., Variational-like inequalities. Optimization. 30 (1994), 323-330.
  • [14] Peˇcari´c, JE., Porschan, F. and Tong, YL., Convex Functions, Partial Orderings and Statistical Applications. Academic Press Inc., 1992.
  • [15] Pini, R., Invexity and generalized convexity. Optimization. 22 (1991), 513-525.
  • [16] Weir, T. and Mond, B., Preinvex functions in multiple objective optimization. J. Math. Anal. Appl. 136 (1998), 29-38.
  • [17] Yang, XM. and Li, D., On properties of preinvex functions. J. Math. Anal. Appl. 256 (2001), 229-241.

Year 2019, Volume: 7 Issue: 1, 54 - 61, 30.04.2019

Huriye Kadakal İmdat İşcan

https://doi.org/10.36753/mathenot.559247

Abstract

References

  • [1] Barani, A., Ghazanfari AG, Dragomir SS. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex. Journal of Inequalities and Applications. 2012 (2012):247.
  • [2] Dragomir, SS. and Pearce, CEM., Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University, 2000.
  • [3] Hadamard, J., Étude sur les propriétés des fonctions entières et en particulier d’une fonction considerée par Riemann. J. Math. Pures Appl. 58 (1893), 171-215.
  • [4] Israel, AB. and Mond, B., What is invexity? J. Aust. Math. Soc.Ser. B. 28 (1986), 1-9.
  • [5] ˙I¸scan, ˙I., Set, E. and Özdemir, ME., On new general integral inequalities for s-convex functions. Applied Mathematics and Computation. 246 (2014), 306-315.
  • [6] ˙I¸scan ˙I., Ostrowski type inequalities for functions whose derivatives are preinvex. Bulletin of the Iranian Mathematical Society. 40 (2014), 2, 373-386.
  • [7] Latif, MA. and Dragomir, SS., Some Hermite-Hadamard type inequalities for functions whose partial derivatives in absloute value are preinvex on the co-oordinates. Facta Universitatis (NIŠ) Ser. Math. Inform. 28 (2013), No. 3, 257-270.
  • [8] Maden, S., Kadakal, H., Kadakal, M. and ˙I ¸scan ˙I., Some new integral inequalities for n-times differentiable convex functions. J. Nonlinear Sci. Appl. 10 (2017), 12, 6141-6148.
  • [9] Matloka, M., On some new inequalities for differentiable (h1; h2)-preinvex functions on the co-ordinates. Mathematics and Statistics. 2 (2014), 1, 6-14.
  • [10] Mohan, SR., Neogy, SK., On invex sets and preinvex functions. J. Math. Anal. Appl. 189 (1995), 901-908.
  • [11] Noor, MA., Hermite-Hadamard integral inequalities for log-preinvex functions. J. Math. Anal. Approx. Theory. 2 (2007), 126-131.
  • [12] Noor, MA., Invex equilibrium problems. J. Math. Anal. Appl. 302 (2005), 463-475.
  • [13] Noor, MA., Variational-like inequalities. Optimization. 30 (1994), 323-330.
  • [14] Peˇcari´c, JE., Porschan, F. and Tong, YL., Convex Functions, Partial Orderings and Statistical Applications. Academic Press Inc., 1992.
  • [15] Pini, R., Invexity and generalized convexity. Optimization. 22 (1991), 513-525.
  • [16] Weir, T. and Mond, B., Preinvex functions in multiple objective optimization. J. Math. Anal. Appl. 136 (1998), 29-38.
  • [17] Yang, XM. and Li, D., On properties of preinvex functions. J. Math. Anal. Appl. 256 (2001), 229-241.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Huriye Kadakal

İmdat İşcan

Publication Date April 30, 2019
Submission Date October 30, 2018
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Kadakal, H., & İşcan, İ. (2019). New Inequalities for Preinvex Functions. Mathematical Sciences and Applications E-Notes, 7(1), 54-61. https://doi.org/10.36753/mathenot.559247
AMA Kadakal H, İşcan İ. New Inequalities for Preinvex Functions. Math. Sci. Appl. E-Notes. April 2019;7(1):54-61. doi:10.36753/mathenot.559247
Chicago Kadakal, Huriye, and İmdat İşcan. “New Inequalities for Preinvex Functions”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 54-61. https://doi.org/10.36753/mathenot.559247.
EndNote Kadakal H, İşcan İ (April 1, 2019) New Inequalities for Preinvex Functions. Mathematical Sciences and Applications E-Notes 7 1 54–61.
IEEE H. Kadakal and İ. İşcan, “New Inequalities for Preinvex Functions”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 54–61, 2019, doi: 10.36753/mathenot.559247.
ISNAD Kadakal, Huriye - İşcan, İmdat. “New Inequalities for Preinvex Functions”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 54-61. https://doi.org/10.36753/mathenot.559247.
JAMA Kadakal H, İşcan İ. New Inequalities for Preinvex Functions. Math. Sci. Appl. E-Notes. 2019;7:54–61.
MLA Kadakal, Huriye and İmdat İşcan. “New Inequalities for Preinvex Functions”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 54-61, doi:10.36753/mathenot.559247.
Vancouver Kadakal H, İşcan İ. New Inequalities for Preinvex Functions. Math. Sci. Appl. E-Notes. 2019;7(1):54-61.
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