A new subclass of uniformly spirallike functions with fixed coefficients

Year 2019, Volume: 68 Issue: 2, 2026 - 2036, 01.08.2019

Geetha Balachandar

https://doi.org/10.31801/cfsuasmas.582163

Abstract

In this paper a new subclass of uniformly spirallike functions is defined and several properties like coefficient estimate, closure theorems, distortion theorems, radii of starlikeness and convexity are studied.

Keywords

Analytic functions, univalent functions, uniformly convex functions, uniformly spirallike functions

References

• Balachandar, Geetha, Fixed coefficients for a new subclass of uniformly spirallike functions, Acta Universitatis Apulensis no. 40, (2014),233--243.
• Goodman, A. W., On uniformly convex functions, Ann. Polon. Math. 56 no. 1, (1991), 87--92.
• Goodman, A. W., On uniformly starlike functions, J. Math. Anal. Appl. 155 no. 2, (1991), 364--370.
• Kanas, S. and Wiśniowska, A., Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105 no. 1-2, (1999), 327--336.
• Kanas, S. and Wiśniowska, A,. Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl. 45 (2000), no. 4 (2001), 647--657.
• Wan Cang, Ma and David,. Minda, Uniformly convex functions. Ann. Polon. Math. 57no. 2, (1992), 165--175.
• Ravichandran, V., Selvaraj, C. and R. Rajagopal, On uniformly convex spiral functions and uniformly spirallike functions, Soochow J. Math. 29 no. 4, (2003), 393--405.
• Frode, R., Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118 no. 1, (1993), 189--196.
• Schild, A. and Silverman, H., Convolutions of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Skłodowska Sect. A 29 (1975), 99--107.
• Selvaraj, C. and Geetha, R., On subclasses of uniformly convex spirallike functions and corresponding class of spirallike functions, Int. J. Contemp. Math. Sci. 5 no. 37-40, (2010), 1845--1854.
• Selvaraj, C. and Geetha, R., On uniformly spirallike functions and a corresponding subclass of spirallike functions, Glo. J. Sci. Front. Res., 10 (2010), 36--41.
• Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109--116.
• Silverman, H. and Silvia, E. M., Fixed coefficients for subclasses of starlike functions, Houston J. Math. 7 no. 1, (1981), 129--136.