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Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex

Year 2022, Volume: 10 Issue: 1, 73 - 78, 15.04.2022

Abstract

In this paper, we prove a new integral identity. Basing on this identity, we establish some new dual Simpson-type inequalities for functions whose absolute value of the first derivatives are preinvex. Applications are also given.

References

  • [1] H. Budak, F. Usta and M. Z. Sarikaya, New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacet. J. Math. Stat. 47 (2018), no. 3, 567–578.
  • [2] H. Budak, F. Usta and M. Z. Sarikaya, Refinements of the Hermite-Hadamard inequality for co-ordinated convex mappings. J. Appl. Anal. 25 (2019), no. 1, 73–81.
  • [3] H. Budak, F. Usta, M. Z. Sarikaya and M. E. Ozdemir, On generalization of midpoint type inequalities with generalized fractional integral operators. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 113 (2019), no. 2, 769–790.
  • [4] Lj. Dedi´c, M. Mati´c and J. Peˇcari´c, On dual Euler-Simpson formulae. Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 3, 479–504.
  • [5] M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80 (1981), no. 2, 545–550.
  • [6] P. T. Harker, Generalized Nash games and quasi-variational inequalities. European journal of Operational research 54 (1991), no.1, 81-94.
  • [7] B. Meftah, Two dimensional Cˇ ebysˇev type inequalities for functions whose second derivatives are co-ordinated (h1;h2)-preinvex. Konuralp J. Math. 6 (2018), no. 1, 76-83.
  • [8] B. Meftah, Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are prequasiinvex via power mean inequality. J. Appl. Anal. 25 (2019), no 1, 83-90.
  • [9] B. Meftah and C. Marrouche, Some new Hermite-Hadamard type inequalities for n-times log-convex functions. Jordan J. Math. Stat. 14(2021), no. 4, 651-669.
  • [10] B. B. Mordukhovich and J. V. Outrata, Coderivative analysis of quasi-variational inequalities with applications to stability and optimization. SIAM J. Optim. 18 (2007), no. 2, 389–412.
  • [11] A. Nagurney, Finance and variational inequalities. Quant. Finance 1 (2001), no. 3, 309–317.
  • [12] M. A. Noor, Variational-like inequalities. Optimization 30 (1994), no. 4, 323–330.
  • [13] M. A. Noor, Invex equilibrium problems. J. Math. Anal. Appl. 302 (2005), no. 2, 463–475.
  • [14] J. Peˇcari´c, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992.
  • [15] R. Pini, Invexity and generalized convexity. Optimization 22 (1991), no. 4, 513–525.
  • [16] F. Usta, H. Budak, M. Z. Sarikaya and E. Set, On a generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators. Filomat 32 (2018), no. 6, 2153–2171.
  • [17] F. Usta and M. Z. Sarikaya, On generalization conformable fractional integral inequalities. Filomat 32 (2018), no. 16, 5519–5526.
  • [18] F. Usta and M. Z. Sarikaya, On bivariate retarded integral inequalities and their applications. Facta Univ. Ser. Math. Inform. 34 (2019), no. 3, 553–561.
  • [19] F. Usta, H. Budak and M. Z. Sarikaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 113 (2019), no. 2, 1059–1080.
  • [20] F. Usta, H. Budak and M. Z. Sarikaya, Some new Chebyshev type inequalities utilizing generalized fractional integral operators. AIMS Math. 5 (2020), no. 2, 1147–1161.
  • [21] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization. J. Math. Anal. Appl. 136 (1988), no. 1, 29–38.
  • [22] X. -M. Yang and D. Li, On properties of preinvex functions. J. Math. Anal. Appl. 256 (2001), no. 1, 229–241.
  • [23] G. X. -Z.Yuan, G. Isac, K. -K. Tan and J. Yu, The study of minimax inequalities, abstract economics and applications to variational inequalities and Nash equilibria. Acta Appl. Math. 54 (1998), no. 2, 135–166.
Year 2022, Volume: 10 Issue: 1, 73 - 78, 15.04.2022

Abstract

References

  • [1] H. Budak, F. Usta and M. Z. Sarikaya, New upper bounds of Ostrowski type integral inequalities utilizing Taylor expansion. Hacet. J. Math. Stat. 47 (2018), no. 3, 567–578.
  • [2] H. Budak, F. Usta and M. Z. Sarikaya, Refinements of the Hermite-Hadamard inequality for co-ordinated convex mappings. J. Appl. Anal. 25 (2019), no. 1, 73–81.
  • [3] H. Budak, F. Usta, M. Z. Sarikaya and M. E. Ozdemir, On generalization of midpoint type inequalities with generalized fractional integral operators. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 113 (2019), no. 2, 769–790.
  • [4] Lj. Dedi´c, M. Mati´c and J. Peˇcari´c, On dual Euler-Simpson formulae. Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 3, 479–504.
  • [5] M. A. Hanson, On sufficiency of the Kuhn-Tucker conditions. J. Math. Anal. Appl. 80 (1981), no. 2, 545–550.
  • [6] P. T. Harker, Generalized Nash games and quasi-variational inequalities. European journal of Operational research 54 (1991), no.1, 81-94.
  • [7] B. Meftah, Two dimensional Cˇ ebysˇev type inequalities for functions whose second derivatives are co-ordinated (h1;h2)-preinvex. Konuralp J. Math. 6 (2018), no. 1, 76-83.
  • [8] B. Meftah, Fractional Ostrowski type inequalities for functions whose certain power of modulus of the first derivatives are prequasiinvex via power mean inequality. J. Appl. Anal. 25 (2019), no 1, 83-90.
  • [9] B. Meftah and C. Marrouche, Some new Hermite-Hadamard type inequalities for n-times log-convex functions. Jordan J. Math. Stat. 14(2021), no. 4, 651-669.
  • [10] B. B. Mordukhovich and J. V. Outrata, Coderivative analysis of quasi-variational inequalities with applications to stability and optimization. SIAM J. Optim. 18 (2007), no. 2, 389–412.
  • [11] A. Nagurney, Finance and variational inequalities. Quant. Finance 1 (2001), no. 3, 309–317.
  • [12] M. A. Noor, Variational-like inequalities. Optimization 30 (1994), no. 4, 323–330.
  • [13] M. A. Noor, Invex equilibrium problems. J. Math. Anal. Appl. 302 (2005), no. 2, 463–475.
  • [14] J. Peˇcari´c, F. Proschan and Y. L. Tong, Convex functions, partial orderings, and statistical applications. Mathematics in Science and Engineering, 187. Academic Press, Inc., Boston, MA, 1992.
  • [15] R. Pini, Invexity and generalized convexity. Optimization 22 (1991), no. 4, 513–525.
  • [16] F. Usta, H. Budak, M. Z. Sarikaya and E. Set, On a generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators. Filomat 32 (2018), no. 6, 2153–2171.
  • [17] F. Usta and M. Z. Sarikaya, On generalization conformable fractional integral inequalities. Filomat 32 (2018), no. 16, 5519–5526.
  • [18] F. Usta and M. Z. Sarikaya, On bivariate retarded integral inequalities and their applications. Facta Univ. Ser. Math. Inform. 34 (2019), no. 3, 553–561.
  • [19] F. Usta, H. Budak and M. Z. Sarikaya, Montgomery identities and Ostrowski type inequalities for fractional integral operators. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 113 (2019), no. 2, 1059–1080.
  • [20] F. Usta, H. Budak and M. Z. Sarikaya, Some new Chebyshev type inequalities utilizing generalized fractional integral operators. AIMS Math. 5 (2020), no. 2, 1147–1161.
  • [21] T. Weir and B. Mond, Pre-invex functions in multiple objective optimization. J. Math. Anal. Appl. 136 (1988), no. 1, 29–38.
  • [22] X. -M. Yang and D. Li, On properties of preinvex functions. J. Math. Anal. Appl. 256 (2001), no. 1, 229–241.
  • [23] G. X. -Z.Yuan, G. Isac, K. -K. Tan and J. Yu, The study of minimax inequalities, abstract economics and applications to variational inequalities and Nash equilibria. Acta Appl. Math. 54 (1998), no. 2, 135–166.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Tarek Chiheb This is me

Badreddine Meftah 0000-0002-0156-7864

Amel Dih This is me

Publication Date April 15, 2022
Submission Date March 5, 2022
Acceptance Date April 25, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Chiheb, T., Meftah, B., & Dih, A. (2022). Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex. Konuralp Journal of Mathematics, 10(1), 73-78.
AMA Chiheb T, Meftah B, Dih A. Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex. Konuralp J. Math. April 2022;10(1):73-78.
Chicago Chiheb, Tarek, Badreddine Meftah, and Amel Dih. “Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives Are Preinvex”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 73-78.
EndNote Chiheb T, Meftah B, Dih A (April 1, 2022) Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex. Konuralp Journal of Mathematics 10 1 73–78.
IEEE T. Chiheb, B. Meftah, and A. Dih, “Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex”, Konuralp J. Math., vol. 10, no. 1, pp. 73–78, 2022.
ISNAD Chiheb, Tarek et al. “Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives Are Preinvex”. Konuralp Journal of Mathematics 10/1 (April 2022), 73-78.
JAMA Chiheb T, Meftah B, Dih A. Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex. Konuralp J. Math. 2022;10:73–78.
MLA Chiheb, Tarek et al. “Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives Are Preinvex”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 73-78.
Vancouver Chiheb T, Meftah B, Dih A. Dual Simpson Type Inequalities for Functions Whose Absolute Value of the First Derivatives are Preinvex. Konuralp J. Math. 2022;10(1):73-8.
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