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Journals / Sigma Journal of Engineering and Natural Sciences / 2026 / Volume: 37 Issue: 2

n-TIMES DIFFERENTIABLE PREINVEX AND PREQUASIINVEX FUNCTIONS

Huriye Kadakal(Bulancak Bahçelievler Anatolian High School)0000-0002-0304-7192
Pages
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Publication Date
2019-06-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, the results we obtained in this article coincide with the previous ones in special cases.

📌 3 Key Takeaways

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Objective & Hypothesis:In this manuscript, a new identity for functions defined on an open invex subset of set of real numbers is established.
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Key Findings & Data:We present new type integral inequalities for functions whose powers of nth derivatives in absolute value are preinvex and prequasiinvex functions.
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Conclusion & Impact:Moreover, the results we obtained in this article coincide with the previous ones in special cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Invex set · preinvex function · prequasiinvex function

Abstract

In this manuscript, a new identity for functions defined on an open invex subset of set of real numbers is established. We present new type integral inequalities for functions whose powers of nth derivatives in absolute value are preinvex and prequasiinvex functions. This paper is a generalization of studies being done for functions whose first, second, third and fourth derivatives are preinvex and prequasiinvex. Moreover, the results we obtained in this article coincide with the previous ones in special cases.

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Cite This Article

Kadakal, H. (2019). n-TIMES DIFFERENTIABLE PREINVEX AND PREQUASIINVEX FUNCTIONS. Sigma Journal of Engineering and Natural Sciences, Volume: 37 Issue: 2. https://ajindex.com/articles/1632758

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References (18)

  1. Antczak T., (2005) Mean value in invexity analysis, Nonl. Anal., 60, 1473-1484.
  2. Barani A., (2011) Ghazanfari AG, Dragomir SS. Hermite-Hadamard inequality through prequasiinvex functions, RGMIA Research Report Collection; 14, Article 48, 7 pp.
  3. Barani A., (2012) Ghazanfari AG, Dragomir SS. Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal., 2012:247.
  4. Israel AB. and Mond B. What is invexity? J. Aust. Math. Soc. Ser. B 1986; 28(1), 1-9.
  5. Ion D.A., (2007) Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova, Math. Comp. Sci. Ser., Volume 34, Pages 82–87.
  6. İşcan İ., (2014) Ostrowski type inequalities for functions whose derivatives are preinvex, Bulletin of the Iranian Mathematical Society, 40 (2), 373-386.
  7. Kadakal H., and İşcan İ., (2019) New Integral Inequalities for Preinvex Functions, Mathematical Sciences and Applications, E-Notes, 7 (1) 54-61 (2019).
  8. İşcan İ., Kadakal M. and Kadakal H., (2019) On Two Times Differentiable Preinvex and Prequasiinvex Functions, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., Volume 68, Number 1, Pages 950–963.
  9. Kadakal H., (2019) Differentiable Preinvex and Prequasiinvex Functions, Miskolc Mathematical Notes, (Submitted to journal).
  10. Kadakal H., Kadakal M. and İşcan İ., (2018) New Type Integral Inequalities for Three Times Differentiable Preinvex and Prequasiinvex Functions, Open Journal of Mathematical Analysis, Vol. 2, Issue 1, pp. 33–46.
  11. Kadakal H. and Maden S., (2019). Some Inequalities for Prequasiinvex Functions, Communication in Mathematical Modelling and Applications, CMMA 4, No. 1, 18-24.
  12. Latif M.A. and Dragomir S.S., (2013) 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., Vol. 28, No 3, 257-270.
  13. Matloka M., (2014) On some new inequalities for differentiable (h_1;h_2)-preinvex functions on the co-ordinates, Mathematics and Statistics, 2(1), 6-14.
  14. Mohan S.R. and Neogy S.K., (1995) On invex sets and preinvex functions, J. Math. Anal. Appl., 189, 901-908. Noor M.A., (2007) Hermite-Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory, 2, 126-131.
  15. Noor M.A., (2005) Invex equilibrium problems. J. Math. Anal. Appl, 302, 463-475.
  16. Weir T. and Mond B., (1998) Preinvex functions in multiple objective optimization, J. Math Anal Appl., 136, 29-38.
  17. Yang X.M., Yang X.Q. and Teo K.L., (2003) Generalized invexity and generalized invariant monotonicity, J. Optim. Theory. Appl., 117, 607-625.
  18. Yang X.M. and Li D., (2001) On properties of preinvex functions. J. Math. Anal. Appl., 256, 229-241.