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Quantum Analogues of Hermite–Hadamard Type Inequalities for Generalized Convexity

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Computation, Cryptography, and Network Security

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.

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Acknowledgements

Authors would like to express their gratitude to Prof. Dr. Themistocles M. Rassias for his kind invitation. The authors also would like to thank Dr. S.M. Junaid Zaidi, Rector, COMSATS Institute of Information Technology, Pakistan, for providing excellent research and academic environment. This research is supported by HEC NRPU project No: 20-1966/R&D/11-2553.

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Authors and Affiliations

  1. COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan

    Muhammad Aslam Noor, Khalida Inayat Noor & Muhammad Uzair Awan

Authors
  1. Muhammad Aslam Noor
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  2. Khalida Inayat Noor
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  3. Muhammad Uzair Awan
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Correspondence to Muhammad Aslam Noor .

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Editors and Affiliations

  1. Department of Mathematics and Engineering, Hellenic Military Academy, Vari Attikis, Greece

    Nicholas J. Daras

  2. Department of Mathematics, ETH Zürich, Zürich, Switzerland

    Michael Th. Rassias

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Noor, M.A., Noor, K.I., Awan, M.U. (2015). Quantum Analogues of Hermite–Hadamard Type Inequalities for Generalized Convexity. In: Daras, N., Rassias, M. (eds) Computation, Cryptography, and Network Security. Springer, Cham. https://doi.org/10.1007/978-3-319-18275-9_18

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