Abstract
We consider the generalized preinvex functions, which unify the preinvex and φ-convex functions. We give an account of the quantum integral inequalities via the generalized preinvex functions. Results obtained in this chapter represent significant and important refinements of the known results. These inequalities involve Riemann-type quantum integrals. We would like to emphasize that these results reduce to classical results, when q → 1. It is expected that ideas and techniques given here would inspire further research.
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Acknowledgements
The authors would like to express their sincere gratitude to Dr. S. M. Junaid Zaidi (H.I., S. I. ), Rector, COMSATS Institute of Information Technology, Pakistan, for providing excellent research and academic environment. The authors would also like to express their sincere gratitude to the referee for his constructive suggestions and interest.
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Noor, M.A., Rassias, T.M., Noor, K.I., Awan, M.U. (2017). Quantum Integral Inequalities for Generalized Preinvex Functions. In: Govil, N., Mohapatra, R., Qazi, M., Schmeisser, G. (eds) Progress in Approximation Theory and Applicable Complex Analysis. Springer Optimization and Its Applications, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-49242-1_12
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