IJAM: Volume 37, No. 5 (2024)

DOI: 10.12732/ijam.v37i5.7

GENERALIZED NESTED FUNCTIONS AND

SOME GENERALIZATIONS OF WILKER AND

HUYGEN’S INEQUALITIES

Seyyed Hossein Jafari Petroudi 1,§,

Arsalan Hojjat Ansari 2, Choonkil Park 3

1 Department of Mathematics, Payame Noor University

P.O. Box 19395-3697, Tehran, IRAN

2 Department of Mathematics, Karaj Branch

Islamic Azad University, Karaj, IRAN

Department of Mathematics, Payame Noor University

P.O. Box 19395-3697, Tehran, IRAN

3 Research Institute for Convergence of Basic Science

Hanyang University, Seoul 04763, KOREA

Abstract. In this work, we are using the special case of Mittag-Leffler functions, namely,
H and T Nested Functions Tpj and Hpj. We study some properties and identities of these functions. Then, we derive new results about the generalizations of Wilker and Huygen’s type inequalities based on Tpj and Hpj, with improving some recent inequalities.

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How to cite this paper?
DOI: 10.12732/ijam.v37i5.7
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 5

References

[1] A. H. Ansari, X. Liu, V. N. Mishra, On Mittag-Leffler function and beyond, Nonlinear Sci. Lett. A., 8, No 2 (2017), 187-199.

[2] A. H. Ansari, S. Maksimovic, L. Guran, M. Zhou, Nested functions of type supertrigonometric and superhyperbolic via Mittag-Leffler functions, Ser. A: Appl. Math. Inform. And Mech., 15, No 2 (2023), 109-120.

[3] Y. J. Bagul, C. Chesneau and M. Kostic, On the Cusa-Huygens inequality. HAL Id: hal-02475321 (2020), 1-13.

[4] H. Barsam, Y. Sayyari, S. Mirzadeh, Jensen’s inequality and tgs-convex functions with applications, J. Mahani Math. Res., 12, No 2 (2023), 459-446.

[5] C. P. Chen, and C. Mortici, The relationship between Huygens and Wilker’s inequalities and further remarks, Appl. Anal. Discrete Math., 17 (2023), 92-100.

[6] R. Estrada and M. Pavlovic, L’H.opital’s monotone rule, Gromov’s theorem, and operations that preserve the monotonicity of quotients, Publications de L’institut Mathematique, Nouvelle sґerie, 101, No 115 (2017), 11-24.

[7] L-G. Huang, L. Yin, Y-L. Wang, and X-L. Lin, Some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions, J. Inequal. Appl., 52 (2018), 1-8.

[8] A. Issa and S. Ibrahimov, New identities for hyperbolic Lucs functions, Journal of New Theory., 41 (2022), 51-61.

[9] V. Kiryakova, The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus, Computers and Math. With Appl., 59 (2010), 1885-1895; doi:10.1016/j.camwa.2009.08.025.

[10] S. Kome, Wilker-type inequalities for k-Fibonacci hyperbolic functions, Turk. J. Math. Comput. Sci., 14, No 2 (2022), 340-345.

[11] D. S. Mitrinovic, J. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Springer, Dordrecht (2013).

[12] K. Nantomah, Cusa-Huygens, Wilker and Huygens type inequalities for generalized hyperbolic functions, Earthline Journal of Mathematical Sciences, 5, No 2 (2021), 277-289.

[13] K. Nantomah, E. Prempeh, Some inequalities for generalized hyperbolic functions, Moroccan J. of Pure and Appl. Anal., 6, No 1 (2020), 76-92.

[14] E. Neuman, J. Sandor, On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker and Huygens inequalities, Math. Inequalities & Appl., 13, No 4 (2010), 715-723.

[15] S. H. J. Petroudi and M Pirouz, Toward new class of hyperbolic functions. International Conference on Combinatorics, Cryptography and Computer Science, Tehran, Iran (2022).

[16] S. H. J. Petroudi, C. Park, A. H. Ansari, A. Dasdemir, Nested Functions on Some Generalizations of Wilker and Huygen’s inequalities, Preprint (2024).

[17] A. Sheikhhosseini, Schur multiplier operator and matrix in equalities, J. Mahani Math. Res.,13, No 1 (2023), 383-390; doi:10.22103/jmmr.2023.21383.1434.

[18] A. P. Stakhov, and B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23, No 2 (2005), 379-389.

[19] X.J. Yang, An Introduction to Hypergeometric, Supertrigonometric and Superhyperbolic Functions, Academic Press, Elsevier (2021).

[20] ZH. Yang, YM. Chu, Sharp Wilker-type inequalities with applications, J. Inequal. Appl., 2014, 166 (2014); doi:10.1186/1029-242X-2014-166.

[21] L. Zhu, Inequalities for hyperbolic functions and their applications. J. Inequal and Appl., 2010; doi:10.1155/2010/130821.

[22] L. Zhu, Wilker inequalities of exponential type for circular functions. Rev. Real Acad. Cienc. Exactas Fis. Nat.- A: Mat., 115, 35 (2021); doi:10.1007/s13398-020-00973-6.

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