Year 2019, Volume 7, Issue 1, Pages 54 - 61 2019-04-30

New Inequalities for Preinvex Functions

Huriye Kadakal [1] , İmdat İşcan [2]

20 63

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.
Invex set, preinvex function, Hölder Integral inequality
  • [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.
Primary Language en
Journal Section Articles
Authors

Author: Huriye Kadakal

Author: İmdat İşcan

Dates

Publication Date: April 30, 2019

Bibtex @research article { mathenot559247, journal = {MSAEN}, issn = {}, eissn = {2147-6268}, address = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {54 - 61}, doi = {}, title = {New Inequalities for Preinvex Functions}, key = {cite}, author = {Kadakal, Huriye and İşcan, İmdat} }
APA Kadakal, H , İşcan, İ . (2019). New Inequalities for Preinvex Functions. MSAEN, 7 (1), 54-61. Retrieved from http://dergipark.org.tr/mathenot/issue/44921/559247
MLA Kadakal, H , İşcan, İ . "New Inequalities for Preinvex Functions". MSAEN 7 (2019): 54-61 <http://dergipark.org.tr/mathenot/issue/44921/559247>
Chicago Kadakal, H , İşcan, İ . "New Inequalities for Preinvex Functions". MSAEN 7 (2019): 54-61
RIS TY - JOUR T1 - New Inequalities for Preinvex Functions AU - Huriye Kadakal , İmdat İşcan Y1 - 2019 PY - 2019 N1 - DO - T2 - MSAEN JF - Journal JO - JOR SP - 54 EP - 61 VL - 7 IS - 1 SN - -2147-6268 M3 - UR - Y2 - 2019 ER -
EndNote %0 MSAEN New Inequalities for Preinvex Functions %A Huriye Kadakal , İmdat İşcan %T New Inequalities for Preinvex Functions %D 2019 %J MSAEN %P -2147-6268 %V 7 %N 1 %R %U
ISNAD Kadakal, Huriye , İşcan, İmdat . "New Inequalities for Preinvex Functions". MSAEN 7 / 1 (April 2019): 54-61.
AMA Kadakal H , İşcan İ . New Inequalities for Preinvex Functions. MSAEN. 2019; 7(1): 54-61.
Vancouver Kadakal H , İşcan İ . New Inequalities for Preinvex Functions. MSAEN. 2019; 7(1): 61-54.