| 1 | Abramowitz M , Stegun I A . Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Washington: US Government Printing Office, 1964 | | 2 | Lehto O , Virtanen K I . Quasiconformal Mappings in the Plane. New York: Springer-Verlag, 1973 | | 3 | Anderson G D , Vamanamurthy M K , Vuorinen M . Conformal Invariants, Inequalities, and Quasiconformal Maps. New York: John Wiley & Sons, 1997 | | 4 | András S , Baricz á . Bounds for complete elliptic integrals of the first kind. Expo Math, 2010, 28 (4): 357- 364 | | 5 | Wang M K , Chu Y M , Qiu Y F , Qiu S L . An optimal power mean inequality for the complete elliptic integrals. Appl Math Lett, 2011, 24 (6): 887- 890 | | 6 | Wang G D , Zhang X H , Chu Y M . A power mean inequality for the Gr?tzsch ring function. Math Inequal Appl, 2011, 14 (4): 833- 837 | | 7 | Chu Y M , Wang M K , Qiu S L . Optimal combinations bounds of root-square and arithmetic means for Toader mean. Proc Indian Acad Sci Math Sci, 2012, 122 (1): 41- 51 | | 8 | Wang M K , Chu Y M , Qiu S L , Jiang Y P . Bounds for the perimeter of an ellipse. J Approx Theory, 2012, 164 (7): 928- 937 | | 9 | Chu Y M , Qiu Y F , Wang M K . H?lder mean inequalities for the complete elliptic integrals. Integral Transforms Spec Funct, 2012, 23 (7): 521- 527 | | 10 | Wang G D , Zhang X H , Chu Y M . A power mean inequality involving the complete elliptic integrals. Rocky Mountain J Math, 2014, 44 (5): 1661- 1667 | | 11 | Yang Z H, Qian W M, Chu Y M, Zhang W. Monotonicity rule for the quotient of two functions and its application. J Inequal Appl, 2017, Article: 106 | | 12 | Qian W M, Chu Y M. Sharp bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters. J Inequal Appl, 2017, Article: 274 | | 13 | Yang Z H , Qian W M , Chu Y M , Zhang W . On approximating the arithmetic-geometric mean and complete elliptic integral of the first kind. J Math Anal Appl, 2018, 462 (2): 1714- 1726 | | 14 | Huang T R, Tan S Y, Ma X Y, Chu Y M. Monotonicity properties and bounds for the complete p-elliptic integrals. J Inequal Appl, 2018, Article: 239 | | 15 | Zhao T H, Wang M K, Zhang W, Chu Y M. Quadratic transformation inequalities for Gaussian hypergeometric function. J Inequal Appl, 2018, Article: 251 | | 16 | Yang Z H , Qian W M , Chu Y M . Monotonicity properties and bounds involving the complete elliptic integrals of the first kind. Math Inequal Appl, 2018, 21 (4): 1185- 1199 | | 17 | Yang Z H , Chu Y M , Zhang W . High accuracy asymptotic bounds for the complete elliptic integral of the second kind. Appl Math Comput, 2019, 348, 552- 564 | | 18 | Zhao T H, Zhou B C, Wang M K, Chu Y M. On approximating the quasi-arithmetic mean. J Inequal Appl, 2019, Article: 42 | | 19 | Wang J L, Qian W M, He Z Y, Chu Y M. On approximating the Toader mean by other bivariate means. J Funct Spaces, 2019, Article ID: 6082413 | | 20 | Wang M K , Chu Y M , Zhang W . Monotonicity and inequalities involving zero-balanced hypergeometric function. Math Inequal Appl, 2019, 22 (2): 601- 617 | | 21 | Qiu S L , Ma X Y , Chu Y M . Sharp Landen transformation inequalities for hypergeometric functions, with applications. J Math Anal Appl, 2019, 474 (2): 1306- 1337 | | 22 | Takeuchi S . A new form of the generalized complete elliptic integrals. Kodai Math J, 2016, 39 (1): 202- 226 | | 23 | Drábek P , Manásevich R . On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian. Differential Integral Equations, 1999, 12 (6): 773- 788 | | 24 | Kobayashi H , Takeuchi S . Applications of generalized trigonometric functions with two parameters. Commun Pure Appl Anal, 2019, 18 (3): 1509- 1521 | | 25 | Takeuchi S. Applications of generalized trigonometric functions with two parameters Ⅱ. 2019, arXiv: 1904.01827 | | 26 | Takeuchi S . Legendre-type relations for generalized complete elliptic integrals. J Class Anal, 2016, 9 (1): 35- 42 | | 27 | Takeuchi S . Complete p-elliptic integrals and a computation formula of $\pi_{p}$ for p=4. Ramanujan J, 2018, 46 (2): 309- 321 | | 28 | Wang M K , Zhang W , Chu Y M . Monotonicity, convexity and inequalities involving the generalized elliptic integrals. Acta Math Sci, 2019, 39B (5): 1440- 1450 | | 29 | Wang M K, Chu H H, Chu Y M. Precise bounds for the weighted H?lder mean of the complete p-elliptic integrals. J Math Anal Appl, 2019, 480(2), Article ID: 123388 | | 30 | Huang T R, Han B W, Ma X Y, Chu Y M. Optimal bounds for the generalized Euler-Mascheroni constant. J Inequal Appl 2018, Article: 118 | | 31 | Zaheer Ullah S, Adil Khan M, Chu Y M. A note on generalized convex functions. J Inequal Appl, 2019, Article: 291 | | 32 | Zhang X H . Monotonicity and functional inequalities for the complete p-elliptic integrals. J Math Anal Appl, 2017, 453 (2): 942- 953 | | 33 | Anderson G D , Qiu S L , Vamanamurthy M K , Vuorinen M . Generalized elliptic integrals and modular equations. Pacific J Math, 2000, 192 (1): 1- 37 | | 34 | Baricz á . Turán inequalities for generalized complete elliptic integrals. Math Z, 2007, 256 (4): 895- 911 | | 35 | Anderson G D , Sugawa T , Vamanamurthy M K , Vourinen M . Twice-punctured hyperbolic sphere with a conical singularity and generalized elliptic integral. Math Z, 2010, 266 (1): 181- 191 | | 36 | Neuman E . Inequalities and bounds for generalized complete elliptic integrals. J Math Anal Appl, 2011, 373 (1): 203- 213 | | 37 | Bhayo B A , Vuorinen M . On generalized complete elliptic integrals and modular functions. Proc Edinb Math Soc (2), 2012, 55 (3): 591- 611 | | 38 | Yang Z H , Chu Y M . A monotonicity property involving the generalized elliptic integral of the first kind. Math Inequal Appl, 2017, 20 (3): 729- 735 | | 39 | Wang M K , Li Y M , Chu Y M . Inequalities and infinite product formula for Ramanujan generalized modular equation function. Ramanujan J, 2018, 46 (1): 189- 200 | | 40 | Wang M K , Chu Y M , Zhang W . The precise estimates for the solution of Ramanujan's generalized modular equation. Ramanujan J, 2019, 49 (3): 653- 668 | | 41 | He X H , Qian W M , Xu H Z , Chu Y M . Sharp power mean bounds for two Sándor-Yang means. Rev R Acad Cienc Exactas Fís Nat Ser A Mat, 2019, 113 (3): 2627- 2638 | | 42 | Qian W M, Yang Y Y, Zhang H W, Chu Y M. Optimal two-parameter geometric and arithmetic mean bounds for the Sándor-Yang mean. J Inequal Appl, 2019, Article: 287 | | 43 | Bullen P S . Handbook of Means and Their Inequalities. Dordrecht: Kluwer Academic Publishers Group, 2003 | | 44 | Anderson G D , Vamanamurthy M K , Vuorinen M . Generalized convexity and inequalities. J Math Anal Appl, 2007, 335 (2): 1294- 1308 | | 45 | Baricz á. Convexity of the zero-balanced Gaussian hypergeometric functions with respect to H?lder means. JIPAM J Inequal Pure Appl Math, 2007, 8(2), Article: 40 | | 46 | Wang M K , Chu Y M , Qiu S L , Jiang Y P . Convexity of the complete elliptic integrals of the first kind with respect to H?lder means. J Math Anal Appl, 2012, 388 (2): 1141- 1146 | | 47 | Chu Y M , Wang M K , Jiang Y P , Qiu S L . Concavity of the complete elliptic integrals of the second kind with respect to H?lder means. J Math Anal Appl, 2012, 395 (2): 637- 642 | | 48 | Zhou L M , Qiu S L , Wang F . Inequalities for the generalized elliptic integrals with respect to H?lder mean. J Math Anal Appl, 2012, 386 (2): 641- 646 | | 49 | Baricz á , Bhayo B A , Klén R . Convexity properties of generalized trigonometric and hyperbolic functions. Aequationes Math, 2015, 89 (3): 473- 484 | | 50 | Baricz á , Bhayo B A , Vuorinen M . Turán inequalities for generalized inverse trigonometric functions. Filomat, 2015, 29 (2): 303- 313 |
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