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

Muhammad Uzair Awan (), Muhammad Aslam Noor, Khalida Inayat Noor, Yu-Ming Chu () and Sara Ellahi
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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

A chapter in Approximation and Computation in Science and Engineering, 2022, pp 927-944 from Springer

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-84122-5_43

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DOI: 10.1007/978-3-030-84122-5_43

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