Univalence of certain integral operators involving generalized Struve functions

Abstract

In this paper, we are mainly interested to find sufficient conditions for some integral operators defined by generalized Struve functions. These operators are normalized and as well as univalent in the open unit disc $\mathcal{U}$. Some special cases of Struve functions and modified Struve functions are also a part of our investigations.

Keywords

• Univalence conditions,Integral operators,Generalized Struve functions,Modified Struve functions,Ahlfors-Becker and Becker univalence criteria,Schwarz lemma

References

1. Abramowitz, M. and Stegun, I. A. Handbook of Mathematical Functions (Dover, New York, 1972).
2. Arif, M. and Raza, M. Some properties of an integral operator defined by Bessel functions, Acta Universitatis Apulensis 26, 6974, 2011.
3. Baricz, A., Dimitrov, D.K., Orhan, H. and Yagmur, N. Radii of starlikeness of some special functions, Proc. Amer. Math. Soc. 144(8) 33553367, 2016.
4. Baricz, A. and Frasin, B.A. Univalence of integral operators involving Bessel functions, Appl. Math. Lett., 23, 371276, 2010.
5. Breaz, D. Univalence properties for a general integral operator, Bull. Korean Math. Soc, 46(3), 439446, 2009.
6. Breaz, D., Breaz, N. and Srivastava, H. M. An extension of the univalent condition for a family of integral operators, Appl. Math. Lett. 22, 4144, 2009.
7. Breaz, D. and Güney, H.O. On the univalence criterion of a general integral operator, J. Inequal. Appl. Volume 2008, Article ID 702715, 8 pages, doi:10.1155/2008/702715.
8. Breaz, D., Owa, S. and Breaz, N. A new integral univalent operator, Acta Univ. Apulensis Math. Inform., 16, 1116, 2008.

9. Bulut, S. Univalence preserving integral operators defined by generalized Al-Oboudi dierential operators, An. St. Univ. Ovidius Constata 17, 3750, 2009.
10. Deniz, E. Convexity of integral operators involving generalized Bessel functions, Integral Transforms Spec. Funct. 24(3), 201216, 2013.
11. Deniz, E. On the univalence of two general integral operators, Filomat, 29(7), 15811586, 2015.
12. Deniz, E. Univalence criteria for a general integral operator, Filomat 28(1), 1119, 2014.
13. Deniz, E. and Orhan, H. Loewner chains and univalence criteria related with Ruscheweyh and Slgean derivatives, J. Appl. Anal. Comput. 5(3), 465478, 2015.
14. Deniz, E. and Orhan, H. Some notes on extensions of basic univalence criteria, J. Korean Math. Soc. 48(1), 179189, 2011.
15. Deniz, E. and Orhan, H. Univalence criterion for meromorphic functions and Loewner chains, Appl. Math. Comput. 218(6), 751755, 2011.
16. Deniz, E., Orhan, H. and Srivastava, H.M. Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math. 15(2), 883917, 2011.
17. Frasin, B.A. Some sufficient conditions for certain integral operators, J. Math. Ineq. 2(4), 527535, 2008.
18. Frasin, B.A. Sufficient conditions for integral operator defined by Bessel functions, J. Math. Ineq. 4(2), 301306, 2010.
19. Frasin, B.A. Univalence criteria for general integral operator, Math. Commun. 16, 115124, 2011.
20. Kanas, S. and Srivastava, H.M. Some criteria for univalence related to Ruscheweyh and Salagean derivatives, Complex Variables Theory Appl. 38, 263275, 1999.
21. Kiryakova, V.S., Saigo, M., and Srivastava, H.M. Some criteria for univalence of analytic functions involving generalized fractional calculus operators, Fract. Calc. Appl. Anal. 1 , 79102, 1998.
22. Nehari, Z. Conformal Mapping, (McGraw-Hill, 1952).
23. Olver, F.W.J., Lozier, D.W., Boisvert, R.F. and Clark, C.W. (eds.) NIST Handbook of Mathematical Functions (Cambridge University Press, Cambridge, 2010).
24. Orhan, H. and Yagmur, N. Geometric properties of generalized struve functions, An. Stiinµ. Univ. Al. I. Cuza Iasi. Mat. (N.S.), doi:10.2478/aicu-2014-0007.
25. Pescar, V. Univalence of certain integral operators, Acta Univ. Apulensis Math. Inform., 12, 4348, 2006.
26. Pescar, V. A new generalization of Ahlfors and Beckers criterion of univalence, Bull. Malaysian Math. Soc., 19, 5354, 1996.
27. Pescar, V. On the univalence of an integral operator, Appl. Math. Lett. 23(5), 615619, 2010.
28. Pescar, V. and Breaz, D. On an integral operator, Appl. Math. Lett. 23(5), 625629, 2010.
29. Pascu, N.N. An improvement of Beckers univalence criterion, in: Proceedings of the Commemorative Session: Simion Stoilow (Brasov), 4348, 1987.
30. Raza, M. and Yağmur, N. Some properties of a class of analytic functions defined by generalized Struve functions. Turkish Journal of Mathematics, 39(6), 931944, 2015.
31. Struve, H. Beitrag zur Theorie der Diraction an Fernrö hren, Annalen der Physik und Chemie, 17(13), 10081016, 1882.
32. Yagmur, N. and Orhan, H. Starlikeness and convexity of generalized Struve functions, Abstr. Appl. Anal., Volume 2013, Article ID: 954513, 6 pages, doi:10.1155/2013/954513.
33. Zhang, S. and Jin, J. Computation of Special Functions, (Wiley, New york, 1996).