Kyungpook Mathematical Journal

  • 제59권2호
  • /
  • Pages.277-291
  • /
  • 2019
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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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)
  • 투고 : 2018.02.10
  • 심사 : 2019.04.23
  • 발행 : 2019.06.23
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초록

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.

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참고문헌

  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. https://doi.org/10.2307/2007212
  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. https://doi.org/10.2298/PIM0591093A
  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. https://doi.org/10.1090/S0002-9939-1970-0264084-7
  8. D. A. Brannan, On functions of bounded boundary rotation I, Proc. Edinburg Math. Soc., 16(1968/69), 339-347. https://doi.org/10.1017/S001309150001302X
  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. https://doi.org/10.1090/S0002-9939-1975-0361033-2
  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. https://doi.org/10.4153/CJM-1967-038-0
  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. E. J. Moulis, A generalization of univalent functions with bounded boundary rotation, Trans. Amer. Math. Soc., 174(1972), 369-381. https://doi.org/10.1090/S0002-9947-1972-0320296-1
  16. E. J. Moulis, Generalizations of the Robertson functions, Pacific J. Math., 81(1979), 167-174. https://doi.org/10.2140/pjm.1979.81.167
  17. M. A. Nasr and M. K. Aouf, Starlike function of complex order, J. Natural Sci. Math., 25(1985), 1-12.
  18. K. I. Noor, M. Arif and W. Ul-Haq, Some properties of certain integral operators, Acta Univ. Apulensis Math. Inform., 21(2010), 89-95.
  19. K. I. Noor, N. Khan and M. A. Noor, On generalized Spiral-like analytic functions, Filomat, 28(7)(2014), 1493-1503. https://doi.org/10.2298/FIL1407493N
  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. https://doi.org/10.4064/ap-31-3-311-323
  25. B. Pinchuk, A variational method for functions of bounded boundary rotation, Trans. Amer. Math. Soc., 138(1969), 107-113. https://doi.org/10.1090/S0002-9947-1969-0237761-8
  26. B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math., 10(1971), 6-16. https://doi.org/10.1007/BF02771515
  27. M. S. Robertson, On the theory of univalent functions, Ann. of Math., 37(1936), 374-408. https://doi.org/10.2307/1968451
  28. M. S. Robertson, Coefficients of functions with bounded boundary rotation, Canad. J. Math., 21(1969), 1477-1482. https://doi.org/10.4153/CJM-1969-161-2
  29. M. S. Robertson, Univalent functions f(z) for which zf'(z) is spirallike, Michigan Math. J., 16(1969), 97-101. https://doi.org/10.1307/mmj/1029000208
  30. E. M. Silvia, A note on special classes of p-valent functions, Rocky Mountain J. Math., 9(2)(1979), 365-370. https://doi.org/10.1216/RMJ-1979-9-2-365
  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.