Some Properties of a Generalized Integral Operator

Authors

  • S. Yalçın Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, 16059, Bursa
  • S. R. Swamy Department of Computer Science and Engineering, R.V. College of Engineering, Bengaluru 560059, Karnataka
  • N. Magesh Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu
  • J. Nirmala Department of Mathematics, Maharani's Science College for Women, Bengaluru 560001

DOI:

https://doi.org/10.26713/cma.v12i1.1471

Keywords:

Holomorphic function, dierential subordination, generalized integral operator.

Abstract

The object of the present paper is to derive some properties of holomorphic functions in the open unit disc which are defined by using a new generalized integral operator by applying a lemma due to Miller and Mocanu. Also we mention some interesting consequences of our main results.

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References

F. M. Al-Oboudi and Z. M. Al-Qahtani, Application of differential subordinations to some properties of linear operators, International Journal of Open Problems Complex Analysis 2 (3) (2010), 189 – 202, http://www.i-csrs.org/Volumes/ijopca/vol.2/vol.2.3.3.November.10.pdf.

M. K. Aouf and T. Bulboaca, Subordination and superordination properties of multivalent functions defined by certain integral operators, Journal of the Franklin Institute 347 (2010), 641 – 653, DOI: 10.1016/j.jfranklin.2010.01.001.

M. K. Aouf, A. O. Mostafa and R. El-Ashwah, Sandwich theorems for p-valent functions defined by a certain integral operator, Mathematical and Computer Modelling 53 (2011), 1647 – 1653, DOI: 10.1016/j.mcm.2010.12.030.

M. K. Aouf, Some properties of Noor integral operator of (ní… p¡1)-th order, Matematicki Vesnik 61 (4) (2009), 269 – 279, http://emis.impa.br/EMIS/journals/MV/094/mv09403.pdf.

S. D. Bernardi, Convex and starlike univalent functions, Transactions of American Mathematical Society 135 (1969), 429 – 446, DOI: 10.1090/S0002-9947-1969-0232920-2.

S. S. Bhoosnurmath and S. R. Swamy, Rotaru starlike integral operators, Tamkang Journal of Mathematics 22 (3) (1991), 291 – 297.

T. Bulboaca, M. K. Aouf and R. M. El-Ashwah, Subordination properties of multivalent functions defined by certain integral operator, Banach Journal of Mathematical Analysis 6 (2) (2012), 69 – 85, http://www.kurims.kyoto-u.ac.jp/EMIS/journals/BJMA/tex_v6_n2_a5.pdf.

L. Cotirl a, A differential sandwich theorem for analytic functions defined by the integral operator, Studia Univ. "Babes–bolyai”, Mathematica 54 (2) (2009), 13 – 21, http://www.cs.ubbcluj.ro/~studia-m/2009-2/cotirla.pdf.

T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, Journal of Mathematical Analysis and Applications 38 (1972), 746 – 765, DOI: 10.1016/0022-247X(72)90081-9.

I. B. Jung, Y. C. Kim and H. M. Srivastava, The Hardy space of analytic functions associated with certain one parameter families of integral operator, Journal of Mathematical Analysis and Applications 176 (1993), 138 – 147, DOI: 10.1006/jmaa.1993.1204.

V. Kumar and S. L. Shukla, Jakubowski starlike integral operators, Journal of the Australian Mathematical Society 37 (1984), 117 – 127, DOI: 10.1017/S1446788700021807.

R. J. Libera, Some classes of regular univalent functions, Proceedings of the American Mathematical Society 16 (1965), 755 – 758, DOI: 10.1090/S0002-9939-1965-0178131-2.

S. Miller, Differential inequalities and Caratheodory function, Bulletin of the American Mathematical Society 81 (1975), 79 – 81, DOI: 10.1090/S0002-9904-1975-13643-3.

S. S. Miller and P. T. Mocanu, Second-order differential inequalities in the complex plane, Journal of Mathematical Analysis and Applications 65(2) (1978), 289 – 305, DOI: 10.1016/0022-247X(78)90181-6.

K. I. Noor and M. A. Noor, On integral operators, Journal of Mathematical Analysis and Applications 238 (1999), 341 – 352, DOI: 10.1006/jmaa.1999.6501.

J. Patel and P. Sahoo, Certain subclasses of multivalent analytic functions, Indian Journal of Pure and Applied Mathematics 34 (3) (2003), 487 – 500, https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/2000827e_487.pdf.

J. Patel, Inclusion relations and convolution properties of certain classes of analytic functions defined by a generalized Salagean operator, Bulletin of the Belgian Mathematical Society - Simon Stevin 15 (2008), 33 – 47, DOI: 10.36045/bbms/1203692445.

G. S. Salagean, Subclasses of univalent functions, Complex Analysis, Fifth Romanian-Finnish Sem., Lecture Notes in Mathematics 1013, Springer Verlag (1983), 362 – 372, DOI: 10.1007/BFb0066543.

S. Shams, S. R. Kulkarni and J. M. Jahangiri, Subordination properties of p-valent functions defined by integral operator, International Journal of Mathematics and Mathematical Sciences (2006), 1 – 3, Article ID 94572, DOI: 10.1155/IJMMS/2006/94572.

S. R. Swamy, Sandwich theorems for p-valent functions defined certain integral operators, International Journal of Mathematica Archive 4 (3) (2013), 101 – 107, http://www.ijma.info/index.php/ijma/article/view/1985.

S. R. Swamy, Sandwich theorems for analytic functions defined by new operators, Journal of Global Research in Mathematical Archives 1 (2) (2013), 76 – 85, https://jgrma.info/index.php/jgrma/article/download/21/19.

S. R. Swamy, Some subordination properties of multivalent functions defined by certain integral operators, Journal of Mathematical and Computational Science 3 (2) (2013), 554 – 568, http://scik.org/index.php/jmcs/article/view/839.

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Published

31-03-2021
CITATION

How to Cite

Yalçın, S., Swamy, S. R., Magesh, N., & Nirmala, J. (2021). Some Properties of a Generalized Integral Operator. Communications in Mathematics and Applications, 12(1), 189–198. https://doi.org/10.26713/cma.v12i1.1471

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Research Article