Strong subordination and superordination with sandwich-type theorems using integral operators

Parviz Arjomandinia, Rasoul Aghalary

Abstract


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.

Keywords


univalent function, integral operator, strong differential subordination and superordination

Full Text:

PDF

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




DOI: http://dx.doi.org/10.24193/subbmath.2021.4.06

Refbacks

  • There are currently no refbacks.