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SIMPSON-LIKE INEQUALITIES FOR TWICE DIFFERENTIABLE (s,P)-CONVEX MAPPINGS INVOLVING WITH AB-FRACTIONAL INTEGRALS AND THEIR APPLICATIONS

Author

Listed:
  • XIAOMAN YUAN

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • LEI XU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • TINGSONG DU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

Abstract

First, we establish the parametrized integral identity and its improved version via Atangana–Baleanu (AB) fractional integrals. For the focus of this paper, we utilize the resulting identities to derive a series of Simpson-like integral inequalities for mappings whose second-order derivatives belong to the (s,P)-convexity and (s,P)-concavity in absolute value. And a couple of outcomes, concerning the Simpson-like quadrature formulas, the q-digamma functions and the modified Bessel functions, are introduced as applications separately in the end.

Suggested Citation

  • Xiaoman Yuan & Lei Xu & Tingsong Du, 2023. "SIMPSON-LIKE INEQUALITIES FOR TWICE DIFFERENTIABLE (s,P)-CONVEX MAPPINGS INVOLVING WITH AB-FRACTIONAL INTEGRALS AND THEIR APPLICATIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-31.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:03:n:s0218348x2350024x
    DOI: 10.1142/S0218348X2350024X
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