Abstract
In this paper, our aim is to establish some mean value inequalities for the Fox–Wright functions, such as Turán-type inequalities, Lazarević and Wilker-type inequalities. As applications we derive some new type inequalities for hypergeometric functions and the four-parametric Mittag–Leffler functions. Furthermore, we prove the monotonicity of ratios for sections of series of Fox–Wright functions. The results are also closely connected with Turán-type inequalities. Moreover, some other type inequalities are also presented. At the end of the paper, some problems are stated which may be of interest for further research.
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Acknowledgements
S. M. Sitnik was supported by a State contract of the Russian Ministry of Education and Science (contract No 1.7311.2017/8.9).
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Mehrez, K., Sitnik, S.M. Functional inequalities for the Fox–Wright functions. Ramanujan J 50, 263–287 (2019). https://doi.org/10.1007/s11139-018-0071-2
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DOI: https://doi.org/10.1007/s11139-018-0071-2
Keywords
- Fox–Wright functions
- Hypergeometric functions
- Four-parametric Mittag–Leffler functions
- Turán-type inequalities
- Lazarević and Wilker-type inequalities