SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF MULTIPLIER TRANSFORMATIONS

Seon Hye An; Nak Eun Cho

doi:10.11948/20230145

2024 Volume 14 Issue 2

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(2): 778-791

Next Article Previous Article

Seon Hye An, Nak Eun Cho. SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF MULTIPLIER TRANSFORMATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 778-791. doi: 10.11948/20230145

Citation:

Seon Hye An, Nak Eun Cho. SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF MULTIPLIER TRANSFORMATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 778-791. doi: 10.11948/20230145

SUBORDINATIONS BY CERTAIN UNIVALENT FUNCTIONS ASSOCIATED WITH A FAMILY OF MULTIPLIER TRANSFORMATIONS

Seon Hye An^1,,
Nak Eun Cho^1, ,

1.
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea

Author Bio: Email: ansonhye@gmail.com(S. H. An)
Corresponding author: Email: necho@pknu.ac.kr(N. E. Cho)
Fund Project: This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2019R1I1A3A01050861)

Abstract

Abstract

The purpose of the present paper is to obtain some implications of subordinations by univalent functions in the open unit disk associated with a family of multiplier transformations. Moreover, applications for integral operators are also considered.
- Subordination /
- multivalent function /
- hadamard product /
- integral operator /
- multiplier transformation
MSC: 30C55, 30C80

FullText(HTML)

References

[1]	H. Aaisha Farzana, M. P. Jeyaraman and T. Bulboacă, On certain subordination properties of a linear operator, J. Fract. Calc. Appl., 2021, 12, 148-162. Google Scholar
[2]	S. S. Akanksha, R. N. Ingle, P. T. Reddy and B. Venkateswarlu, Subclass of uniformly convex functions with negative coefficients defined by linear fractional differential operator, J. Fract. Calc. Appl., 2022, 13, 9-20. Google Scholar
[3]	S. H. An, R. Srivastava and N. E. Cho, New approaches for subordination and superordination of multivalent functions associated with a family of linear operators, accepted in Miskolc Math. Notes, 2023. Google Scholar
[4]	A. A. Attiya and M. F. Yassen, Some subordination and superordination results associated with generalized Srivastava-Attiya operator, Filomat, 2017(1), 31, 53-60. Google Scholar
[5]	S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 1969, 135, 429-446. doi: 10.1090/S0002-9947-1969-0232920-2 CrossRef Google Scholar
[6]	T. Bulboacă, Integral operators that preserve the subordination, Bull. Korean Math. Soc., 1997, 32, 627-636. Google Scholar
[7]	T. Bulboacă, Subordination by alpha-convex functions, Kodai Math. J., 2003, 26, 267-278. Google Scholar
[8]	T. Bulboacă, Generalization of a class of nonlinear averaging integral operators, Math. Nachr., 2005, 278(1-2), 34-42. doi: 10.1002/mana.200310224 CrossRef Google Scholar
[9]	J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 2002, 276, 432-445. doi: 10.1016/S0022-247X(02)00500-0 CrossRef Google Scholar
[10]	N. E. Cho and H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, (2003), 37, 39-49. doi: 10.1016/S0895-7177(03)80004-3 CrossRef Google Scholar
[11]	N. E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate, Turkish. J. Math., 2018, 42, 1380-1399. Google Scholar
[12]	N. E. Cho, Sushil Kumar, V. Kumar and V. Ravichandran, Starlike functions related to the Bell numbers, Symmetry, 2019, 11, Article No. 219. doi: 10.3390/sym11020219 CrossRef Google Scholar
[13]	E. Deniz, M. Kamali and S. Korkmaz, A certain subclass of bi-univalent functions associated with Bell numbers and q-Srivastava Attiya operator, AIMS Math., 2020, 5(6), 7259-7271. doi: 10.3934/math.2020464 CrossRef Google Scholar
[14]	R. M. El-Ashwah and W. Y. Kota, Some properties for certain multivalent functions associated with differ-integral operator and extended multiplier transformations, J. Fract. Calc. Appl., 2021, 12, 85-93. Google Scholar
[15]	R. M. Goel and N. S. Sohi, A new criterion for p-valent functions, Proc. Amer. Math. Soc., 1980, 78, 353-357. Google Scholar
[16]	D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman Publishing Limited, London, 1984. Google Scholar
[17]	I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 1993, 176, 138-147. doi: 10.1006/jmaa.1993.1204 CrossRef Google Scholar
[18]	S. S. Kumar, V. Kumar and V. Ravichandran, Subordination and superordination for multivalent functions defined by linear operators, Tamsui Oxf. J. Inf. Math. Sci., 2013, 29(3), 361-387. Google Scholar
[19]	R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 1965, 16, 755-758. doi: 10.1090/S0002-9939-1965-0178131-2 CrossRef Google Scholar
[20]	J. -L. Liu, The Noor integral and strongly starlike functions, J. Math. Anal. Appl., 2001, 261, 441-447. doi: 10.1006/jmaa.2001.7489 CrossRef Google Scholar
[21]	J. -L. Liu and K. I. Noor, Some properties of Noor integral operator, J. Nat. Geom., 2002, 21, 81-90. Google Scholar
[22]	S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 1981, 28, 157-172. Google Scholar
[23]	S. S. Miller and P. T. Mocanu, Differential Subordination, Theory and Application, Marcel Dekker, Inc., New York, Basel, 2000. Google Scholar
[24]	S. S. Miller, P. T. Mocanu and M. O. Reade, Subordination-preserving integral operators, Trans. Amer. Math. Soc., 1984, 283, 605-615. doi: 10.1090/S0002-9947-1984-0737887-4 CrossRef Google Scholar
[25]	A. O. Mostafa, T. Bulboacă and M. K. Aouf, Sandwich results for multivalent functions defined by generalized Srivastava-Attiya operator, J. Fract. Calc. Appl., 2023, 14(2), Paper No. 2, 11 pp. Google Scholar
[26]	A. Naik, T. Panigrahi and G. Murugusundaramoorthy, Coefficient estimate for class of meromorphic bi-Bazilevič type functions associated with linear operator defined by convolution, Jordan J. Math. Stat., 2021, 14, 287-305. Google Scholar
[27]	K. I. Noor, On new classes of integral operators, J. Natur. Geom., 1999, 16, 71-80. Google Scholar
[28]	K. I. Noor and M. A. Noor, On integral operators, J. Math. Anal. Appl., 1999, 238, 341-352. Google Scholar
[29]	M. O. Oluwayemi and K. Vijaya, On a study of a class of functions associated with a multiplier transformation, Int. J. Math. Comput. Sci., 2022, 17, 931-935. Google Scholar
[30]	S. Owa and H. M. Srivastava, Some applications of the generalized Libera integral operator, Proc. Japan Acad. Ser. A Math. Sci., 1986, 62, 125-128. Google Scholar
[31]	S. Owa and H. M. Srivastava, Some subordination theorems involving a certain family of integral operators, Integral Transforms Spec. Funct., 15, 2004, 445-454. Google Scholar
[32]	Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Göttingen, 1975. Google Scholar
[33]	S. Porwal and S. Kumar, New subclasses of bi-univalent functions defined by multiplier transformation, Stud. Univ. Babeş-Bolyai Math., 2020, 65, 47-55. Google Scholar
[34]	J. K. Prajapat and S. P. Goyal, Applications of Srivastava-Attiya operator to the class of strongly starlike and strongly convex functions, J. Math. Ineq., 2009, 3, 129-137. Google Scholar
[35]	G. S. Sǎlǎgean, Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag), 1983, 1013, 362-372. Google Scholar
[36]	H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct., 2007, 18, 207-216. Google Scholar
[37]	B. A. Uralegaddi and C. Somanatha, Certain classes of univalent functions, Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, 1992, 371-374. Google Scholar