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On approximating the arc lemniscate functions

Author

Listed:
  • Tie-Hong Zhao

    (Hangzhou Normal University)

  • Wei-Mao Qian

    (Huzhou Vocational & Technical College)

  • Yu-Ming Chu

    (Huzhou University)

Abstract

This paper deals with the arc lemniscate functions from the point view of bivariate means which have been introduced in [1]. In this study, several optimal bounds for these bivariate means in terms of arithmetic, geometric and quadratic means are established. As a consequence, new bounds for the arc lemniscate functions are also derived, which improve some previously known results.

Suggested Citation

  • Tie-Hong Zhao & Wei-Mao Qian & Yu-Ming Chu, 2022. "On approximating the arc lemniscate functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 316-329, June.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:2:d:10.1007_s13226-021-00016-9
    DOI: 10.1007/s13226-021-00016-9
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    References listed on IDEAS

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    1. Wang, Miao-Kun & Chu, Yu-Ming & Song, Ying-Qing, 2016. "Asymptotical formulas for Gaussian and generalized hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 44-60.
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    Cited by:

    1. Muhammad Bilal Khan & Hakeem A. Othman & Michael Gr. Voskoglou & Lazim Abdullah & Alia M. Alzubaidi, 2023. "Some Certain Fuzzy Aumann Integral Inequalities for Generalized Convexity via Fuzzy Number Valued Mappings," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    2. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    3. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Hermite–Hadamard Inequalities for Convex Fuzzy-Number-Valued Mappings via Fuzzy Riemann Integrals," Mathematics, MDPI, vol. 10(18), pages 1-18, September.
    4. Muhammad Bilal Khan & Gustavo Santos-García & Muhammad Aslam Noor & Mohamed S. Soliman, 2022. "New Class of Preinvex Fuzzy Mappings and Related Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-20, October.

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