Voir la notice de l'article provenant de la source Math-Net.Ru
@article{PA_2013_2_2_a4, author = {B. A. Bhayo and J. S\'andor}, title = {Inequalities connecting generalized trigonometric functions with their inverses}, journal = {Problemy analiza}, pages = {82--90}, publisher = {mathdoc}, volume = {2}, number = {2}, year = {2013}, language = {en}, url = {http://geodesic.mathdoc.fr/item/PA_2013_2_2_a4/} }
B. A. Bhayo; J. Sándor. Inequalities connecting generalized trigonometric functions with their inverses. Problemy analiza, Tome 2 (2013) no. 2, pp. 82-90. http://geodesic.mathdoc.fr/item/PA_2013_2_2_a4/
[1] Sandor J., “On certain inequalities for hyperbolic and trigonometric functions”, J. Math. Ineq http://files.ele-math.com/preprints/jmi-1062-pre.pdf | MR
[2] Lindqvist P., “Some remarkable sine and cosine functions”, Ricerche di Matematica, XLIV (1995), 269–290 | MR | Zbl
[3] Bhayo B. A., Vuorinen M., Inequalities for eigenfunctions of the $p$-Laplacian, 23 pp., January 2011, arXiv: 1101.3911[math.CA] | MR
[4] Bushell P. J., Edmunds D. E., “Remarks on generalised trigonometric functions”, Rocky Mountain J. Math., 42:1 (2012), 25–57 | DOI | MR | Zbl
[5] Biezuner R. J., Ercole G., Martins E. M., “Computing the first eigenvalue of the $p$-Laplacian via the inverse power method”, J. Funct. Anal., 257:1 (2009), 243–270 | DOI | MR | Zbl
[6] Drabek P., Manasevich R., “On the closed solution to some $p$-Laplacian nonhomogeneous eigenvalue problems”, Differential Integral Equations, 12:6 (1999), 773–788 | MR | Zbl
[7] Klen R., Vuorinen M., Zhang X., Inequalities for the generalized trigonometric and hyperbolic functions, 12 pp., October 2012, arXiv: 1210.6749 | MR
[8] Lang J., Edmunds D. E., Eigenvalues, Embeddings and Generalised Trigonometric Functions, Lecture Notes in Mathematics, Springer-Verlag, 2011 | DOI | MR
[9] Lindqvist P., Peetre J., “$p$-arclength of the $q$-circle”, The Mathematics Student, 72:1-4, (2003), 139-145 | MR | Zbl
[10] Bhayo B. A., Vuorinen M., “On generalized trigonometric functions with two parameters”, J. Approx. Theory, 164 (2012), 1415–1426 | DOI | MR | Zbl
[11] Edmunds D. E., Gurka P., Lang J., “Properties of generalized trigonometric functions”, J. Approx. Theory, 164 (2012), 47–56 | DOI | MR | Zbl
[12] Takeuchi S., “Generalized Jacobian elliptic functions and their application to bifurcation problems associated with $p$-Laplacian”, J. Math. Anal. Appl., 385 (2012), 24–35 | DOI | MR | Zbl
[13] Baricz A. , Bhayo B. A., Vuorinen M., Turan type inequalities for generalized inverse trigonometric functions, 10 pp., May 2013, arXiv: 1305.0938[math.CA]
[14] Klen R., Visuri M., Vuorinen M., “On Jordan type inequalities for hyperbolic functions”, J. Ineq. Appl., 2010 (2010), 14 pp. | MR
[15] Anderson G. D., Vamanamurthy M. K., Vuorinen M., Conformal invariants, inequalities and quasiconformal maps, J. Wiley, 1997, 505 pp. | MR
[16] Kuczma M., An introduction to the theory of functional equations and inequalities. Cauchy's equation and Jensen's inequality. With a Polish summary, Prace Naukowe Uniwersytetu Slaskiego w Katowicach [Scientific Publications of the University of Silesia], 489, Uniwersytet Ślaski, Katowice; Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1985, 523 pp. | MR | Zbl
[17] Sroysang B., “Inequalities for the incomplete beta function”, Mat. Aeterna, 3:4 (2013), 241–244 | MR
[18] Nauka, 1979
[19] Baricz A., “Functional inequalities involving special functions II”, J. Math. Anal. Appl., 327:2 (2007), 1202–1213 | DOI | MR | Zbl
[20] Carlson B. C., “Some inequalities for hypergeometric functions”, Proc. of Amer. Math. Soc., 17:1 (1966), 32–39 | DOI | MR | Zbl
[21] Y.-M Chu, Y.-P Jiang and M.-Kun Wang, Inequalities for generalized trigonometric and hyperbolic sine functions, 7 pp., December 2012, arXiv: 1212.4681
[22] W.-D. Jiang and F. Qi., Geometric convexity of the generalized sine and the generalized hyperbolic sine, arXiv: 1301.3264