Some Interpolation Inequalities Involving Real Valued Functions of a Single Variable
Abstract
Mathematical Inequalities play a critical role in Mathematics and especially in the field of Mathematical analysis. In this work, interpolation estimates involving Lebesgue functional norms are employed to obtain inequalities involving real-valued functions of a single variable. The inequalities involve elementary functions such as polynomials, exponentials and trigonometric functions.
References
Bercu, G. (2016). Padé approximant related to remarkable inequalities involving trigonometric functions. Journal of Inequalities and Applications, 2016, Article 99. https://doi.org/10.1186/s13660-016-1044-x
Bercu, G., & Wu, S. (2016). Refinements of certain hyperbolic inequalities via the Padé approximation method. Journal of Nonlinear Sciences and Applications, 9, 5011–5020. https://doi.org/10.22436/jnsa.009.07.05
Chen, X., & Zhang, L. (2017). Padé approximant related to inequalities involving the constant e and a generalized Carleman-type inequality. Journal of Inequalities and Applications, 2017, Article 205. https://doi.org/10.1186/s13660-017-1479-8
Zhang, L., & Xuesi, M. (2020). New refinements and improvements of some trigonometric inequalities based on Padé approximant. Journal of Mathematics, 2020, Article 2753691, 7 pp. https://doi.org/10.1155/2020/2753691
Bercu, C. (2017). The natural approach of trigonometric inequalities—Padé approximant. Journal of Mathematical Inequalities, 11, 181–191. https://doi.org/10.7153/jmi-11-18
Bagul, Y. J. (2017). Inequalities involving circular, hyperbolic and exponential functions. Journal of Mathematical Inequalities, 11(3). https://doi.org/10.7153/jmi-11-55
Bagul, Y. J., & Chesneau, C. (2019). Some new simple inequalities involving exponential, trigonometric and hyperbolic functions. Cubo A Mathematical Journal, 21(1). https://doi.org/10.4067/S0719-06462019000100021
Bagul, Y. J., Dhaigude, R. M., Kostić, M., & Chesneau, C. (2021). Polynomial-exponential bounds for some trigonometric and hyperbolic functions. Axioms, 10(4), Article 308. https://doi.org/10.3390/axioms10040308
Qi, F. (1997). A method of constructing inequalities about e^x. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat., 8, 16–23.
Menteshashvili, N., Berikashvili, I., & Kvaratskhelia, L. (2023). On an exponential inequality. Bulletin of TICMI, 27(1), 3–8.
Chen, X.-D., Ma, J., & Li, Y. (2019). Approximating trigonometric functions by using exponential inequalities. Journal of Inequalities and Applications, 2019, Article 53. https://doi.org/10.1186/s13660-019-1992-z
Kasuga, N., Nakasuji, M., Nishizawa, Y., & Sekine, T. (2023). Sharpened Jordan's type inequalities with exponential approximations. Journal of Mathematical Inequalities, 17(4), 1539–1550. https://doi.org/10.7153/jmi-2023-17-101
Mahmoud, A., & Anis, M. (2021). Some Padé approximations and inequalities for the complete elliptic integrals of the first kind. Journal of Inequalities and Applications, 2021, Article 37. https://doi.org/10.1186/s13660-021-02568-0
Zhen, Z., Huaqing, S., & Ligeng, C. (2018). Refining trigonometric inequalities by using Padé approximant. Journal of Inequalities and Applications, 2018, Article 149. https://doi.org/10.1186/s13660-018-1742-7
This work is licensed under a Creative Commons Attribution 4.0 International License.