与星象函数有关的拟共形近于凸调和映射

王智刚, 黄心中, 刘志宏, Rahim KARGAR

数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 565-576.

PDF(693 KB)
PDF(693 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (6) : 565-576. DOI: 10.12386/A2020sxxb0048
论文

与星象函数有关的拟共形近于凸调和映射

    王智刚1, 黄心中2, 刘志宏3, Rahim KARGAR4
作者信息 +

On Quasiconformal Close-to-Convex Harmonic Mappings Involving Starlike Functions

    Zhi Gang WANG1, Xin Zhong HUANG2, Zhi Hong LIU3, Rahim KARGAR4
Author information +
文章历史 +

摘要

讨论了一类解析部分为星象函数的拟共形近于凸调和映射的基本性质,得到了此类映射的系数不等式、积分表达式、增长定理、面积定理与部分和的近于凸半径.

Abstract

In this paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an area theorem, and radii of close-to-convexity of partial sums of the class, are derived.

关键词

解析函数 / 单叶函数 / 星象函数 / 近于凸调和映射 / 拟共形调和映射

Key words

analytic function / univalent function / starlike function / close-to-convex harmonic mapping / quasiconformal harmonic mapping

引用本文

导出引用
王智刚, 黄心中, 刘志宏, Rahim KARGAR. 与星象函数有关的拟共形近于凸调和映射. 数学学报, 2020, 63(6): 565-576 https://doi.org/10.12386/A2020sxxb0048
Zhi Gang WANG, Xin Zhong HUANG, Zhi Hong LIU, Rahim KARGAR. On Quasiconformal Close-to-Convex Harmonic Mappings Involving Starlike Functions. Acta Mathematica Sinica, Chinese Series, 2020, 63(6): 565-576 https://doi.org/10.12386/A2020sxxb0048

参考文献

[1] Abu Muhanna Y., Ponnusamy S., Extreme points method and univalent harmonic mappings, In:Complex Analysis and Dynamical Systems VI. Part 2, 223-237, Contemp. Math., 667, Israel Math. Conf. Proc., Amer. Math. Soc., Providence, RI, 2016.
[2] Bshouty D., Joshi S. S., Joshi S. B., On close-to-convex harmonic mappings, Complex Var. Elliptic Equ., 2013, 58:1195-1199.
[3] Bshouty D., Lyzzaik A., Close-to-convexity criteria for planar harmonic mappings, Complex Anal. Oper. Theory, 2011, 5:767-774.
[4] Bshouty D., Lyzzaik A., Sakar F. M., Harmonic mappings of bounded boundary rotation, Proc. Amer. Math. Soc., 2018, 146:1113-1121.
[5] Chen S., Ponnusamy S., Rasila A., et al., Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mapping, Acta Math. Sin. Engl. Ser., 2016, 32:297-308.
[6] Chen J., Rasila A., Wang X., Coefficient estimates and radii problems for certain classes of polyharmonic mappings, Complex Var. Elliptic Equ., 2015, 60:354-371.
[7] Chuaqui M., Hernández R., Harmonic univalent mappings and linearly connected domains, J. Math. Anal. Appl., 2007, 332:1189-1194.
[8] Clunie J., Sheil-Small T., Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A. I Math., 1984, 9:3-25.
[9] Duren P., Harmonic Mappings in the Plane, Cambridge University Press, Cambridge, 2004.
[10] Ghosh N., Vasudevarao A., On a subclass of harmonic close-to-convex mappings, Monatsh. Math., 2019, 188:247-267.
[11] Kalaj D., Quasiconformal harmonic mappings and close-to-convex domains, Filomat, 2010, 24:63-68.
[12] Kalaj D., Ponnusamy S., Vuorinen M., Radius of close-to-convexity and fully starlikeness of harmonic mappings, Complex Var. Elliptic Equ., 2014, 59:539-552.
[13] Kanas S., Maharana S., Prajapat J. K., Norm of the pre-Schwarzian derivative, Bloch's constant and coefficient bounds in some classes of harmonic mappings, J. Math. Anal. Appl., 2019, 474:931-943.
[14] Kaplan W., Close-to-convex schlicht functions, Michigan Math. J., 1952, 1:169-185.
[15] Kargar R., Pascu N. R., Ebadian A., Locally univalent approximations of analytic functions, J. Math. Anal. Appl., 2017, 453:1005-1021.
[16] Koh N. T., Hereditary convexity for harmonic homeomorphisms, Indiana Univ. Math. J., 2015, 64:231-243.
[17] Koh N. T., Harmonic mappings with hereditary starlikeness, J. Math. Anal. Appl., 2018, 457:273-286.
[18] Li L., Ponnusamy S., Injectivity of sections of univalent harmonic mappings, Nonlinear Anal., 2013, 89:276-283.
[19] Li L., Ponnusamy S., Disk of convexity of sections of univalent harmonic functions, J. Math. Anal. Appl., 2013, 408:589-596.
[20] Li L., Ponnusamy S., Sections of stable harmonic convex functions, Nonlinear Anal., 2015, 123-124:178-190.
[21] Li L., Ponnusamy S., On the generalized Zalcman functional λan2-a2n-1 in the close-to-convex family, Proc. Amer. Math. Soc., 2017, 145:833-846.
[22] Lewy H., On the non-vanishing of the Jacobian in certain one-to-one mappings, Bull. Amer. Math. Soc., 1936, 42:689-692.
[23] Long B. Y., Huang H. Y., Radii of harmonic mappings in the plane, J. Aust. Math. Soc., 2017, 102:331-347.
[24] Maharana S., Prajapat J. K., Srivastava H. M., The radius of convexity of partial sums of convex functions in one direction, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 2017, 87:215-219.
[25] Mocanu P. T., Three-cornered hat harmonic functions, Complex Var. Elliptic Equ., 2009, 54:1079-1084.
[26] Mocanu P. T., Injectivity conditions in the complex plane, Complex Anal. Oper. Theory, 2011, 5:759-766.
[27] Nagpal S., Ravichandran V., A subclass of close-to-convex harmonic mappings, Complex Var. Elliptic Equ., 2014, 59:204-216.
[28] Nagpal S., Ravichandran V., Starlikeness, convexity and close-to-convexity of harmonic mappings, In:Current Topics in Pure and Computational Complex Analysis, 201-214, Trends Math., Birkhäuser/Springer, New Delhi, 2014.
[29] Obradovi? M., Ponnusamy S., Wirths K. J., Coefficient characterizations and sections for some univalent functions, Sib. Math. J., 2013, 54:679-696.
[30] Partyka D., Sakan K., Zhu J. F., Quasiconformal harmonic mappings with the convex holomorphic part, Ann. Acad. Sci. Fenn. Math., 2018, 43:401-418.
[31] Ponnusamy S., Rajasekaran S., New sufficient conditions for starlike and univalent functions, Soochow J. Math., 1995, 21:193-201.
[32] Ponnusamy S., Sahoo S. K., Norm estimates for convolution transforms of certain classes of analytic functions, J. Math. Anal. Appl., 2008, 342:171-180.
[33] Ponnusamy S., Sairam Kaliraj A., On harmonic close-to-convex functions, Comput. Methods Funct. Theory, 2012, 12:669-685.
[34] Ponnusamy S., Sairam Kaliraj A., Univalent harmonic mappings convex in one direction, Anal. Math. Phys., 2014, 4:221-236.
[35] Ponnusamy S., Sairam Kaliraj A., Constants and characterization for certain classes of univalent harmonic mappings, Mediterr. J. Math., 2015, 12:647-665.
[36] Ponnusamy S., Sairam Kaliraj A., Starkov V. V., Sections of univalent harmonic mappings, Indag. Math. (N. S.), 2017, 28:527-540.
[37] Ponnusamy S., Sharma N. L., Wirths K. J., Logarithmic coefficients of the inverse of univalent functions, Results Math., 2018, 73:Art. 160.
[38] Singh R., Singh S., Some sufficient conditions for univalence and starlikeness, Collect. Math., 1982, 47:309-314.
[39] Sun Y., Jiang Y. P., Rasila A., On a subclass of close-to-convex harmonic mappings, Complex Var. Elliptic Equ., 2016, 61:1627-1643.
[40] Sun Y., Rasila A., Jiang Y. P., Linear combinations of harmonic quasiconformal mappings convex in one direction, Kodai Math. J., 2016, 39:366-377.
[41] Wang Z. G., Liu Z. H., Li Y. C., On the linear combinations of harmonic univalent mappings, J. Math. Anal. Appl., 2013, 400:452-459.
[42] Wang Z. G., Liu Z. H., Rasila A., et al., On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings, Rocky Mountain J. Math., 2018, 48:1345-1358.
[43] Wang Z. G., Shi L., Jiang Y. P., On harmonic K-quasiconformal mappings associated with asymmetric vertical strips, Acta Math. Sin. Engl. Ser., 2015, 31:1970-1976.

基金

国家自然科学基金资助项目(11961013);湖南省教育厅重点项目(19A097)

PDF(693 KB)

Accesses

Citation

Detail

段落导航
相关文章

/