Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (3): 270-287.doi: 10.13371/j.cnki.chin.q.j.m.2024.03.005

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Ostrowski’s Type Inequalities for Generalized (h,m)−Preinvex Functions with Its Applications

  

  1. School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China
  • Received:2023-03-06 Online:2024-09-30 Published:2024-09-30
  • Contact: LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications. E-mail:liantieyan@sust.edu.cn
  • About author: LI Ran (1997-), female, native of Kaifeng, Henan, graduate student of Shaanxi University of Science & Technology, engages in fuzzy integral and its applications; LIAN Tie-yan (1978-), female, native of Weinan, Shaanxi, associate professor of Shaanxi University of Science & Technology, M.S.D., engages in fuzzy integral and its applications.
  • Supported by:
    Supported by the National Natural Science Foundation of China (Grant No. 11801342) and the Natural Science Foundation of Shaanxi Province (Grant No. 2023-JC-YB-043).

Abstract: A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

Key words: Generalized (h,m)?preinvex function, Hermite?Hadamard inequality, Ostrowski inequality, Simpson inequality

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