Quantum Analogues of Hermite–Hadamard Type Inequalities for Generalized Convexity

Muhammad Aslam Noor (), Khalida Inayat Noor () and Muhammad Uzair Awan ()
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Muhammad Aslam Noor: COMSATS Institute of Information Technology
Khalida Inayat Noor: COMSATS Institute of Information Technology
Muhammad Uzair Awan: COMSATS Institute of Information Technology

A chapter in Computation, Cryptography, and Network Security, 2015, pp 413-439 from Springer

Abstract: Abstract In this chapter, we discuss quantum calculus and generalized convexity. We briefly discuss some basic concepts and results regarding quantum calculus. Some quantum analogues of derivatives and integrals on finite intervals are discussed. After this we move towards generalized convexity. Examples are given to illustrate the importance and significance of generalized convex sets and generalized convex functions. We establish some quantum Hermite–Hadamard inequalities for generalized convexity. Results proved in this paper may stimulate further research activities.

Keywords: Generalized convexity; Integral inequalities; Quantum inequality; Hermite-Hadmard inequalities; Simpson inequalities; Examples (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-18275-9_18

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DOI: 10.1007/978-3-319-18275-9_18

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