Geodesic
Generalized Gudermannian function
Problemy analiza, Tome 7 (2018) no. 1, pp. 70-86.

Voir la notice de l'article provenant de la source Math-Net.Ru

Wilker and Huygens-type inequalities involving generalized Gudermannian function and its inverse function are established. These results are obtained with the aid of the $p$-version of the Schwab–Borchardt mean. Generalized one-parameter trigonometric and hyperbolic functions play a crucial role in this paper.
Keywords: Generalized Gudermannian function and its inverse function; generalized trigonometric and generalized hyperbolic functions; Gauss hypergeometric function; $p$-version of the Schwab–Borchardt mean; inequalities. 
@article{PA_2018_7_1_a4,
     author = {Edward Neuman},
     title = {Generalized {Gudermannian} function},
     journal = {Problemy analiza},
     pages = {70--86},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2018_7_1_a4/}
}
TY  - JOUR
AU  - Edward Neuman
TI  - Generalized Gudermannian function
JO  - Problemy analiza
PY  - 2018
SP  - 70
EP  - 86
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2018_7_1_a4/
LA  - en
ID  - PA_2018_7_1_a4
ER  - 
%0 Journal Article
%A Edward Neuman
%T Generalized Gudermannian function
%J Problemy analiza
%D 2018
%P 70-86
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2018_7_1_a4/
%G en
%F PA_2018_7_1_a4
Edward Neuman. Generalized Gudermannian function. Problemy analiza, Tome 7 (2018) no. 1, pp. 70-86. http://geodesic.mathdoc.fr/item/PA_2018_7_1_a4/

[1] Anderson G. D., Vamanamurthy M. K., Vuorinen M., “Monotonicity rules in calculus”, Amer. Math. Monthly, 133:9 (2006), 805–816 | DOI | MR

[2] Baricz A., Bhayo B. A., Klén R., “Convexity properties of generalized trigonometric and hyperbolic functions”, Aequat. Math., 2013 | DOI | MR

[3] Bhayo B. A., Vuorinen M., “On generalized trigonometric functions with two parameters”, J. Approx. Theory, 164:10 (2012), 1415–1426 | DOI | MR | Zbl

[4] Bhayo B. A., Vuorinen M., “Inequalities for eigenfunctions of the pLaplacian”, Probl. Anal. Issues Anal., 2(20):1 (2013), 13–35 | DOI | MR

[5] Edmunds D. E., Gurka P., Lang J., “Properties of generalized trigonometric functions”, J. Approx. Theory, 164 (2012), 47–56 | DOI | MR | Zbl

[6] Klén R., Vuorinen M., Zhang X., “Inequalities for the generalized trigonometric and hyperbolic functions”, J. Math. Anal. Appl., 409 (2014), 521–529 | DOI | MR | Zbl

[7] Lindqvist P., “Some remarkable sine and cosine functions”, Ricerche di Matematica, 44:2 (1995), 269–290 | MR | Zbl

[8] Neuman E., “Inequalities for weighted sums of powers and their applications”, Math. Inequal. Appl., 15:4 (2012), 995–1005 | MR | Zbl

[9] Neuman E., “Inequalities involving generalized trigonometric and generalized hyperbolic functions”, J. Math. Inequal., 8:4 (2014), 725–736 | DOI | MR | Zbl

[10] Neuman E., “On the inequalities for generalized trigonometric functions”, Int. J. Anal., 2014 (2014), 319837, 5 pp. | MR

[11] Neuman E., “On the p-version of the Schwab-Borchardt mean”, Int. J. Math. Math. Sci., 2014 (2014), 697643, 7 pp. | DOI | MR | Zbl

[12] Neuman E., “On the p-version of the Schwab-Borchardt mean II”, Int. J. Math. Math. Sci., 2015 (2015), 351742, 4 pp. | DOI | MR | Zbl

[13] Neuman E., “Inequalities for the generalized trigonometric, hyperbolic and Jacobian elliptic functions”, J. Math. Inequal., 9:3 (2015), 709–726 | DOI | MR | Zbl

[14] Neuman E., “Wilker and Huygens-type inequalities for Jacobian elliptic and theta functions”, Integral Transforms Spec. Funct., 25:3 (2014), 240–248 | DOI | MR | Zbl

[15] Neuman E., “Wilker and Huygens-type inequalities involving Gudermannian and the inverse Gudermannian functions”, Probl. Anal. Issues Anal., 6(24):1 (2017), 46–57 | DOI | MR | Zbl

[16] Olver F. W. J., Lozier D. W., Boisvert R. F., Clark C. W. (eds.), The NIST Handbook of Mathematical Functions, Cambridge Univ. Press, New York, 2010 | MR