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On G(σ, h)-Convexity of the Functions and Applications to Hermite-Hadamard’s Inequality

In: Approximation and Computation in Science and Engineering

Author

Listed:
  • Muhammad Uzair Awan

    (Government College University Faisalabad)

  • Muhammad Aslam Noor

    (COMSATS University Islamabad)

  • Khalida Inayat Noor

    (COMSATS University Islamabad)

  • Yu-Ming Chu

    (Huzhou University)

  • Sara Ellahi

    (COMSATS University Islamabad)

Abstract

The aim of this chapter is to introduce the notion of G(σ, h)-convex functions a generalized exponentially (σ, h)-convex functions. We show that for suitable choices of real function h(.), the class of G(σ, h)-convex functions reduces to some other new classes of Gσ-convex functions. We also show that for G = exp $${\mathrm {G}}=\exp $$ , we have another new class which is called as G(σ, h)-convex function. For the applications of this class we derive some new variants of Hermite-Hadamard’s inequality using the class of G(σ, h)-convex functions. In the last section, we define the class of strongly G(σ, h)-convexity. We also derive a new Hermite-Hadamard like inequality involving strongly G(σ, h)-convexity. Several new special cases which can be deduced from the main results of the chapter are also discussed.

Suggested Citation

  • Muhammad Uzair Awan & Muhammad Aslam Noor & Khalida Inayat Noor & Yu-Ming Chu & Sara Ellahi, 2022. "On G(σ, h)-Convexity of the Functions and Applications to Hermite-Hadamard’s Inequality," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Approximation and Computation in Science and Engineering, pages 927-944, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-84122-5_43
    DOI: 10.1007/978-3-030-84122-5_43
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