Some classes involving a convolution of analytic functions with some univalency conditions
DOI:
https://doi.org/10.24193/subbmath.2025.2.04Keywords:
Convolution, univalent functions, Dzoik-Srivastava operator, Srivastava-Attiya linear operator, Owa and Srivastava fractional differintegral operator, Jung-Kim-Srivastava integral operatorAbstract
In this paper, involving a convolution f ∗ g, two classes of normalized analytic functions f are defined. Showing an inclusion relation between these classes, various sufficient conditions for functions to be in these classes are established. In particular, varied forms of univalency conditions of the convolution function f ∗ g are given which lead to some univalency conditions of several linear operators.
Mathematics Subject Classification (2010): 30C45, 30C55.
Received 19 November 2024; Accepted 11 April 2025.
References
1. Adegani, E.A., Bulboaca, T., Motamednezhad, A., Sufficient condition for p-valent strongly starlike functions, J. Contemp. Mathemat. Anal., 55(2020), 213-223.
2. Ali, R.M., Ravichandran, V., Seenivasagan, N., Sufficient conditions for Janowski starlikeness, Int. J. Math. Math. Sci., 2007, Art. ID 62925, 7 pp.
3. Baricz, A., Ponnusamy, S., Starlikeness and convexity of generalized Bessel functions, Integral Transforms Spec. Funct., 21(9)(2010), 641-651.
4. Cho, N.E., Srivastava, H.M., Adegani, E.A., Motamednezhad, A., Criteria for a certain class of the Carathéodory functions and their applications, J. Inequal. Appl., 85(2020).
5. Dziok, J., Srivastava, H.M., Classes of analytic functions associated with the generalized hypergeometric functions, Appl. Math. Comput., 103(1999), 1-13.
6. Janowski, W., Some extremal problems for certain families of analytic functions I, Ann. Polon. Math., 28(1973), 297-326.
7. Jung, I.B., Kim, Y.C., Srivastava, H.M., The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., 176(1993), 138-147.
8. Miller, S.S., Mocanu, P.T., Differential Subordinations, Theory and Applications, Marcel Dekker, New York, Basel, 2000.
9. Owa, S., On the distortion theorems I, Kyungpook Math. J., 18(1978), 53-59.
10. Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.
11. Ozaki, S., Nunokawa, M., The Schwartzian derivative and univalent functions, Proc. Amer. Math. Soc., 33(2)(1972), 392-394.
12. Ponnusamy, S., Vuorinen, M., Univalence and convexity properties for Gaussian hyper- geometric functions, Rocky Mountain J. Math., 31(2001), 327-353.
13. Prajapat, J.K., Some sufficient conditions for certain class of analytic and multivalent functions, Southeast Asian Bull. Math., 34(2010), 357-363.
14. Prajapat, J.K., Certain geometric properties of normalized Bessel functions, Appl. Math. Lett., 24(2011), 2133-2139.
15. Raina, R.K., Sharma, P., Subordination preserving properties associated with a class of operators, Le Math., 68(1)(2013), 217-228.
16. Raina, R.K., Sharma, P., Subordination properties of univalent functions involving a new class of operators, Electr. J. Math. Anal. Appl., 2(1)(2014), 37-52.
17. Robertson, M.S., On the theory of univalent functions, Ann. Math., 37(1936), 374-408.
18. Sharma, P., Raina, R.K., Sokoł, J., Certain subordination results involving a class of operators, Analele Univ. Oradea Fasc. Matematica, 21(2)(2014), 89-99.
19. Srivastava, H.M., Attiya, A.A., An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct., 18(2007), 207-216.
20. Srivastava, H.M., Choi, J., Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, London, 2001.
21. Szasz, R., Kupan, P.A., About the univalence of Bessel functions, Stud. Univ. Babeș-Bolyai Math., 54(2009), no. 1, 127-132.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution 4.0 International License.
