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http://dx.doi.org/10.5666/KMJ.2019.59.2.277

Spirallike and Robertson Functions of Complex Order with Bounded Boundary Rotations  

Ahuja, Om (Department of Mathematical Sciences, Kent State University)
Cetinkaya, Asena (Department of Mathematics and Computer Sciences, Istanbul Kultur University)
Kahramaner, Yasemin (Department of Mathematics, Istanbul Ticaret University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.2, 2019 , pp. 277-291 More about this Journal
Abstract
Using the concept of bounded boundary rotation, we investigate various properties of two new generalized classes of spirallike and Robertson functions of complex order with bounded boundary rotations.
Keywords
bounded boundary rotation; ${\lambda}$-spirallike function; ${\lambda}$-Robertson function; integral operator;
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1 L. V. Ahlfors, Sufficient conditions for quasiconformal extension, Ann. Math. Studies 79, Princeton Univ. Press, Princeton, N.J., 1974.
2 O. P. Ahuja, The Bieberbach conjecture and its impact on the developments in geometric function theory, Math. Chronicle, 15(1986), 1-28.
3 O. P. Ahuja and H. Silverman, A survey on spiral-like and related function classes, Math. Chronicle, 20(1991), 39-66.
4 J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math., 17(1915), 12-22.   DOI
5 F. M. Al-Oboudi and M. M. Haidan, Spirallike functions of complex order, J. Natural Geom., 19(2000), 53-72.
6 M. K. Aouf, F. M. Al-Oboudi and M. M. Haidan, On some results for ${\lambda}$-Spirallike and ${\lambda}$-Robertson functions of complex order, Publ. De L'Institut Math., 77(91)(2005), 93-98.   DOI
7 T. Basgoze and F. R. Keogh, The Hardy class of a spiral-like function and its derivative, Proc. Amer. Math. Soc., 26(1970), 266-269.   DOI
8 D. A. Brannan, On functions of bounded boundary rotation I, Proc. Edinburg Math. Soc., 16(1968/69), 339-347.   DOI
9 D. Breaz and N. Breaz, Two integral operators, Studia Univ. Babes-Bolyai Math., 47(2002), 13-19.
10 D. Breaz, S. Owa and N. Breaz, A new integral univalent operator, Acta Univ. Apulensis Math. Inform., 16(2008), 11-16.
11 P. N. Chichra, Regular functions f(z) for which zf'(z) is ${\alpha}$-Spiral-like, Proc. Amer. Math. Soc., 49(1975), 151-160.   DOI
12 O. Lehto, On the distortion of conformal mappings with bounded boundary rotation, Ann. Acad. Sci. Fennicae. Ser. AI Math.-Phys., 124(1952). 14 pp.
13 R. J. Libera, Univalent ${\alpha}$-Spiral functions, Canad. J. Math., 19(1967), 449-456.   DOI
14 C. Loewner, Untersuchungen uber die Verzerrung bei konformen Abbildungen des Einheitskreises $\left|z\right|<1$, die durch Funktionen mit nicht verschwindender Ableitung geliefert werden, Ber. Verh. Sachs. Gess. Wiss. Leipzig, 69(1917), 89-106.
15 K. I. Noor, M. Arif and W. Ul-Haq, Some properties of certain integral operators, Acta Univ. Apulensis Math. Inform., 21(2010), 89-95.
16 E. J. Moulis, A generalization of univalent functions with bounded boundary rotation, Trans. Amer. Math. Soc., 174(1972), 369-381.   DOI
17 E. J. Moulis, Generalizations of the Robertson functions, Pacific J. Math., 81(1979), 167-174.   DOI
18 M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natural Sci. Math., 25(1985), 1-12.
19 K. I. Noor, N. Khan and M. A. Noor, On generalized Spiral-like analytic functions, Filomat, 28(7)(2014), 1493-1503.   DOI
20 K. I. Noor, B. Malik and S. Mustafa, A survey on functions of bounded boundary and bounded radius rotation, Appl. Math. E-Notes, 12(2012), 136-152.
21 L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pest. Mat., 62(1932), 12-19.
22 V. Paatero, Uber die konforme Abbildung von Gebieten deren Rander von beschrankter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A, 33(1931), 1-77.
23 V. Paatero, Uber Gebiete von beschrankter Randdrehung, Ann. Acad. Sci. Fenn. Ser. A, 37(1933), 1-20.
24 K. S. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31(3)(1975/76), 311-323.   DOI
25 B. Pinchuk, A variational method for functions of bounded boundary rotation, Trans. Amer. Math. Soc., 138(1969), 107-113.   DOI
26 B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math., 10(1971), 6-16.   DOI
27 E. M. Silvia, A note on special classes of p-valent functions, Rocky Mountain J. Math., 9(2)(1979), 365-370.   DOI
28 M. S. Robertson, On the theory of univalent functions, Ann. of Math., 37(1936), 374-408.   DOI
29 M. S. Robertson, Coefficients of functions with bounded boundary rotation, Canad. J. Math., 21(1969), 1477-1482.   DOI
30 M. S. Robertson, Univalent functions f(z) for which zf'(z) is spirallike, Michigan Math. J., 16(1969), 97-101.   DOI
31 P. G. Umarani, Functions of bounded boundary rotation of complex order, Math. Balkanica, 3(1989), 34-43.
32 P. Wiatrowski, The coefficients of a certain family of holomorphic functions, Zeszyty Nauk. Univ. Lodz. Nauki. Math. Przyrod. Ser. II, 39(1971), 75-85.