대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제37권4호
  • /
  • Pages.995-1007
  • /
  • 2022
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

PROPERTIES OF FUNCTIONS WITH BOUNDED ROTATION ASSOCIATED WITH LIMAÇON CLASS

  • 투고 : 2021.08.10
  • 심사 : 2022.02.07
  • 발행 : 2022.10.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, we initiate subclasses of functions with boundary and radius rotations that are related to limaçon domains and examine some of their geometric properties. Radius results associated with functions in these classes and their linear combination are studied. Furthermore, the growth rate of coefficients, arc length and coefficient estimates are derived for these novel classes. Overall, some useful consequences of our findings are also illustrated.

키워드

참고문헌

  1. S. Afis and K. I. Noor, On subclasses of functions with boundary and radius rotations associated with crescent domains, Bull. Korean Math. Soc. 57 (2020), no. 6, 1529-1539. https://doi.org/10.4134/BKMS.b200039
  2. N. E. Cho, V. Kumar, and V. Ravichandran, Arc length for Janowski classes, An. Stiint. Univ. Al. I. Cuza Ia,si. Mat. (N.S.) 65 (2019), no. 1, 91-105. https://doi.org/10.1007/s41980-018-0127-5
  3. P. L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften, 259, Springer-Verlag, New York, 1983.
  4. A. W. Goodman, Univalent functions, Mariner Comp. 1983.
  5. S. Hussain and K. Ahmad, On strongly starlike and strongly convex functions with bounded radius and bounded boundary rotation, J. Inequal. Appl. 2020 (2020), no. 126, 10 pp. https://doi.org/10.1186/s13660-020-02391-z
  6. K. Lowner, Untersuchungen Uber die Verzerrung bei konformen Abbildungen des Ein-heitskreises, die durch Funktionen mit nicht verschwindender Ableitung geliefert werden, Verh. Sachs. Ges. Wiss. Leipzig 69 (1917), 89-106.
  7. V. S. Masih and S. Kanas, Subclasses of starlike and convex functions associated with the limacon domain, Symmetry 12 (2020), no. 6, 942. https://doi.org/10.3390/sym12060942
  8. K. I. Noor, On analytic functions related with functions of bounded boundary rotation, Comment. Math. Univ. St. Paul. 30 (1981), no. 2, 113-118.
  9. K. I. Noor, Some properties of analytic functions with bounded radius rotation, Complex Var. Elliptic Equ. 54 (2009), no. 9, 865-877. https://doi.org/10.1080/17476930902998878
  10. 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.
  11. K. I. Noor, W. Ul-Haq, M. Arif, and S. Mustafa, On bounded boundary and bounded radius rotations, J. Inequal. Appl. 2009 (2009), Art. ID 813687, 12 pp. https://doi.org/10.1155/2009/813687
  12. M. Nunokawa and J. Sok'ol, On a length problem for close-to-convex functions, Studia Sci. Math. Hungar. 55 (2018), no. 3, 293-304. https://doi.org/10.1556/012.2018.55.3.1401
  13. M. Nunokawa, J. Sok'o l, and N. E. Cho, On a length problem for univalent functions, Mathematics 6 (2018), no. 11, 266. https://doi.org/10.3390/math6110266
  14. M. Nunokawa, J. Soko l, and H. Tang, Length problems for Bazilevic functions, Demonstr. Math. 52 (2019), no. 1, 56-60. https://doi.org/10.1515/dema-2019-0007
  15. H. Orhan and D. Raducanu, The Fekete-Szego functional for generalized starlike and convex functions of complex order, Asian-Eur. J. Math. 14 (2021), no. 3, Paper No. 2150036, 10 pp. https://doi.org/10.1142/S1793557121500364
  16. V. Paatero, Uber die konforme Abbildung von Gebieten deren Rander von beschrankter Drehung sind, 33, AG Sana, 1931.
  17. V. Paatero, uber Gebiete von beschrAnkter Randdrehung, Suomalaisen Tiedeakatemian Kustantama, 1933.
  18. B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math. 10 (1971), 6-16. https://doi.org/10.1007/BF02771515
  19. M. I. S. Robertson, On the theory of univalent functions, Ann. of Math. (2) 37 (1936), no. 2, 374-408. https://doi.org/10.2307/1968451
  20. A. Saliu, On generalized k-uniformly close-to-convex functions of Janowski type, Int. J. Anal. Appl. 17 (2019), no. 6, 958-973.
  21. A. Saliu and K. I. Noor, On Janowski close-to-convex functions associated with conic regions, Int. J. Anal. Appl. 18 (2020), no. 4, 614-623.
  22. A. Saliu, K. I. Noor, S. Hussain, and M. Darus, On quantum differential subordination related with certain family of analytic functions, J. Math. 2020 (2020), Art. ID 6675732, 13 pp. https://doi.org/10.1155/2020/6675732
  23. A. Saliu, K. I. Noor, S. Hussain, and M. Darus, Some results for the family of univalent functions related with lima,con domain, AIMS Math. 6 (2021), no. 4, 3410-3431. https://doi.org/10.3934/math.2021204
  24. Y. J. Sim, D. K. Thomas, and P. Zaprawa, The second Hankel determinant for starlike and convex functions of order alpha, Complex Var. Elliptic Equ. 2021 (2021), 1-21. https://doi.org/10.1080/17476933.2021.1931149
  25. J. Sok'o l and M. Nunokawa, On some new length problem for analytic functions, Hacet. J. Math. Stat. 46 (2017), no. 3, 427-435.
  26. R. K. Stump, Linear combinations of univalent functions with complex coefficients, Canadian J. Math. 23 (1971), 712-717. https://doi.org/10.4153/CJM-1971-080-6
  27. L. A. Wani and A. Swaminathan, Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc. 44 (2021), no. 1, 79-104. https://doi.org/10.1007/s40840-020-00935-6
  28. W. Ul-Haq and K. I. Noor, A certain class of analytic functions and the growth rate of Hankel determinant, J. Inequal. Appl. 2012 (2012), 309, 11 pp. https://doi.org/10.1186/1029-242X-2012-309