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On General Local Fractional Integral Inequalities For Generalized H-Preinvex Functions On Yang’S Fractal Sets

Author

Listed:
  • YONG ZHANG

    (School of Mathematics and Statistics, Jishou University, Jishou 416000, P. R. China)

  • WENBING SUN

    (��School of Science, Shaoyang University, Shaoyang 422000, P. R. China)

Abstract

In this paper, based on Yang’s fractal theory, the Hermite–Hadamard’s inequalities for generalized h-preinvex function are proved. Then, using the local fractional integral identity proposed by Sun [Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature, Fractals 27(5) (2019) 1950071] as auxiliary function, some parameterized local fractional integral inequalities for generalized h-preinvex functions are established. For the special cases of the parameters, some generalized Simpson-type, midpoint-type and trapezoidal inequalities are established. Finally, some applications of these inequalities in numerical integration are proposed.

Suggested Citation

  • Yong Zhang & Wenbing Sun, 2024. "On General Local Fractional Integral Inequalities For Generalized H-Preinvex Functions On Yang’S Fractal Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x24400255
    DOI: 10.1142/S0218348X24400255
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