Korean J. Math. Vol. 28 No. 1 (2020) pp.137-147
DOI: https://doi.org/10.11568/kjm.2020.28.1.137

On some classes of spiral-like functions defined by the Salagean operator

Main Article Content

Mohammad Mehdi Shabani
Saeed Hashemi Sababe

Abstract

In this paper, we introduce two subclasses of analytic and Spiral-like functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes.


Article Details

References

[1] O. P. Ahuja, Families of analytic functions related to Ruscheweyh derivatives and subordinate to convex functions, Yokohama Math. J. 41 (1993), 39-50. Google Scholar

[2] V. Arora, S. Ponnusami, S.K. Sahoo, Successive coefficients for spirallike and related functions, arXiv:1903.10232 [math.CV] 2019. Google Scholar

[3] S.S. Bhoosnurmath, M.V. Devadas, Subclasses of spirallike functions defined by subordination, J. of Analysis Madras 4, (1996), 173-183. Google Scholar

[4] S.S. Bhoosnurmath, M.V. Devadas, Subclasses of spirallike functions defined by Ruschweyh derivatives, Tamkang J. Math. 28 (1997), 59-65. Google Scholar

[5] J.H Choi, Applications for certain classes of spirallike functions defined by the Srivastava-Attiya operator, APM 8(6), (2018), 615-623. Google Scholar

[6] R. M. Goel and B. S. Mehrok, On the coefficients of a subclass of starlike functions, Indian J.Pure Appl. Math. 12, (1981), 634-647. Google Scholar

[7] A.W.Goodman, Univalent Functions Vol. I Vol. II Polygonal Oublishing House, Washington,FI, (1983). Google Scholar

[8] S. Hashemi Sababe and A. Ebadian, Some properties of reproducing kernel Banach and Hilbert spaces, SCMA, 12(1) (2018), 167-177. Google Scholar

[9] S. Hashemi Sababe, A. Ebadian and Sh. Najafzadeh, On 2-inner product spaces and reproducing kernel property, TKJM, 49(2) (2018), 143-153. Google Scholar

[10] W. Janowski, Some extremal problems for certain families of analytic functions, Bull. Polish Acad. Sci. 21, (1973), 17-25. Google Scholar

[11] W. Janowski, Some extremal problems for certain families of analytic functions, Annl. Polon.Math. 28, (1973), 297-326. Google Scholar

[12] N. Khan, A. Khan, Q.Z. Ahmad, B. Khan, Study of multivalent spirallike Bazilevic functions, AIMS Mathematics 3(3) (2018), 353-364. Google Scholar

[13] S.V. Nikitin, A class of regular functions, current problems in function theory (Russian) 188, 143-147, Rostov-Gos. Univ. Rostov-on-Don, (1987). Google Scholar

[14] K.I. Noor, Z.H. Bukhari, Some subclasses of analytic and spiral-like functions of complex order involving the SrivastavaAttiya integral operator, INTEGR Trans F SPEC F,1013, 21 (2010), 907-916. Google Scholar

[15] J.A. Rosenfeld, B. Russo and W.E. Dixon The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions, J MATH ANAL APPL, 463(2) (2018), 576-592. Google Scholar

[16] G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math., Springer, Berlin,1013, 362-372, (1983). Google Scholar

[17] T.N. Shanmugam, Convolution And Differential Subordination, Internat. J. Math. Sci. 12, (1989) 333-340. Google Scholar

[18] H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 1, (1985), 48-61. Google Scholar

[19] H. Silverman, Subclasses of starlike functions, Rev. Roumaine. Math. Pures Appl, 231 (1978), 1093-1099. Google Scholar

[20] A. Varsudevararo, FeketeSzeg¨o inequality for certain spiral-like functions, CR MATH. 354(11) (2016), 1065-1070. Google Scholar