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The main objective of this chapter is to introduce the class of generalized biconvex functions. We show that this class relates to several unrelated classes of convexity. We derive several new integral inequalities of the Hermite–Hadamard type essentially using the generalized biconvexity property of the functions. We discuss several special cases, which show that our results are quite unifying.

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Hermite–Hadamard-Like Inequalities Involving Generalized Biconvex Functions

  • 章节

  • 发表日期：

    2025年

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  • Muhammad Uzair Awan,
  • Muhammad Aslam Noor,
  • Muhammad Zakria Javed,
  • Khalida Inayat Noor,
  • Michael Th. Rassias

摘要

The main objective of this chapter is to introduce the class of generalized biconvex functions. We show that this class relates to several unrelated classes of convexity. We derive several new integral inequalities of the Hermite–Hadamard type essentially using the generalized biconvexity property of the functions. We discuss several special cases, which show that our results are quite unifying.