On Wilker’s and Huygen’s Type Inequalities for Generalized Trigonometric and Hyperbolic Functions

Nitin Darkunde; Sanjay Ghodechor

doi:10.17485/IJST/v17i9.3206

Article

On Wilker’s and Huygen’s Type Inequalities for Generalized Trigonometric and Hyperbolic Functions

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i9.3206

Year: 2024, Volume: 17, Issue: 9, Pages: 787-793

Original Article

On Wilker’s and Huygen’s Type Inequalities for Generalized Trigonometric and Hyperbolic Functions

Nitin Darkunde¹, Sanjay Ghodechor^2*

¹Assistant Professor, School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, 431606, Maharashtra, India
²Assistant Professor, School of Computing, MIT ADT University, Pune, 412201, Maharashtra, India

*Corresponding Author
Email: [email protected]

Received Date:22 December 2023, Accepted Date:27 January 2024, Published Date:20 February 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The Trigonometric inequalities, generalized trigonometric inequalities which have been obtained by Wilker and Cusa Huygens have attracted attention of so many researchers. Generalized trigonometric functions are simple generalization of the classical trigonometric functions. It is related to the r- Laplacian, which is known as a non-linear differential operator. Method: For the establishment of inequalities involving generalized trigonometric and hyperbolic functions convexity plays the important role in many aspects, also Monotonicity rule is used for sharpness of inequalities. This technique is used to refine and sharpness of inequalities. Findings: Our main result of this paper focus on generalization of Wilker and Cusa Huygens type inequalities for generalized trigonometric and hyperbolic functions with one parameter. Novelty: The inequalities with generalized trigonometric and hyperbolic functions proved in this research paper are Wilker's and Cusa Huygens generalization. It can be used for further refinement and sharpness.

Keywords: Trigonometric function, Hyperbolic function, Generalized Trigonometric, Hyperbolic functions, Wilker Inequality and Huygen's Inequality

References

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Copyright

© 2024 Darkunde & Ghodechor. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)