Strong subordination and superordination with sandwich-type theorems using integral operators
DOI:
https://doi.org/10.24193/subbmath.2021.4.06Keywords:
univalent function, integral operator, strong differential subordination and superordinationAbstract
The notions of strong differential subordination and superordination have been studied recently by many authors.In the present paper,Using these concepts, we obtain some preserving properties of certain nonlinear integral operator defined onthe space of normalized analytic functions in $\mathbb{D}\times\overline{\mathbb{D}}$. The sandwich-type theorems and consequences of the main results are also considered.References
bibitem{1.a} Antonino, J. A., {it Strong differential subordination and applications to univalency conditions}, J. Korean Math. Soc., {bf 43}, 311-322, 2006.
bibitem{2.a} Bulboaca, T.,{it A class of double subordination-preserving integral operators}, Pure Math. Appl., {bf 15}, 87-106, 2004.
bibitem{3.a} Cho, N. E., {it Sandwich-type theorems for a class of nonlinear integral operators}, Proceeding book of the international symposium on geometric function theory and applications, 25-38, 2007.
bibitem{4.a} Cho, N. E. and Bulboaca, T., {it Subordination and superordination properties for a class of integral operators}, Acta Math. Sinica, {bf 26}, 515-522, 2010.
bibitem{5.a} Duren, P. L., {em Univalent functions}, Springer-Verlag, New York, 1983.
bibitem{6.a} Jeyaraman, M. P. and Suresh, T. K., {it Strong differential subordination and superordination of analytic functions}, J. Math. Anal. Appl., {bf 385}, 854-864, 2012.
bibitem{7.a} Miller, S. S., Mocanu, P. T., emph{Differential subordinations, theory and applications}, Marcel Dekker, Jnc., New York, 2000.
bibitem{8.a} Oros, Gh., {it Briot-Bouquet strong differential superordinations and sandwich theorems}, Math. reports, {bf 12 (62)}, 277-283, 2010.
bibitem{11.a} Oros, G. I., {it On a new strong differential subordination}, Acta Univ. Apulensis, {bf 32}, 243-250, 2012.
bibitem{9.a} Oros, G. I. and Oros, Gh., {it Strong differential subordination}, Turkish journal of mathematics, {bf 33}, 249-257, 2009.
bibitem{10.a} Raina, R. K. and Sharma, P., {it Subordination preserving properties associated with a class of operators}, Le Matematiche, vol. LXVIII, 217-228, 2013
Downloads
Additional Files
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.