대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권3호
  • /
  • Pages.657-671
  • /
  • 2024
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

MULTIVALENT NON-CARATHÉODORY FUNCTIONS INVOLVING HIGHER ORDER DERIVATIVES

  • Daniel Breaz (Department of Mathematics "1 Decembrie 1918" University of Alba Iulia) ;
  • Kadhavoor Ragavan Karthikeyan (Department of Applied Mathematics and Science College of Engineering National University of Science & Technology) ;
  • Sakkarai Lakshmi (Department of Information Technology University of Technology and Applied Sciences) ;
  • Alagiriswamy Senguttuvan (Department of Applied Mathematics and Science College of Engineering National University of Science & Technology)
  • 투고 : 2023.06.30
  • 심사 : 2024.03.20
  • 발행 : 2024.07.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we use higher order derivatives with regard to symmetric points to introduce a class of multivalent starlike functions. The major deviation is that we define some differential characterizations that are subordinate to a function whose real part is not greater than zero. The primary outcomes of this study are initial coefficients and the Fekete-Szegő inequality for functions falling under the given class. Also, we have obtained an interesting subordination results involving symmetric functions. The results obtained here extend or unify the various other well-known and new results.

키워드

과제정보

The authors are grateful to the reviewer for the valuable remarks, comments, and advices that help us to remove some mistakes that appeared in the manuscript and to improve the quality of the paper.

참고문헌

  1. M. K. Aouf, Certain subclasses of p-valent starlike functions defined by using a differential operator, Appl. Math. Comput. 206 (2008), no. 2, 867-875. https://doi.org/10.1016/j.amc.2008.09.048 
  2. M. K. Aouf, Some families of p-valent functions with negative coefficients, Acta Math. Univ. Comenian. (N.S.) 78 (2009), no. 1, 121-135. 
  3. M. K. Aouf, Bounded p-valent Robertson functions defined by using a differential operator, J. Franklin Inst. 347 (2010), no. 10, 1927-1941. https://doi.org/10.1016/j.jfranklin.2010.10.012 
  4. M. K. Aouf, T. Bulboaca, and T. Seoudy, Subclasses of multivalent non-Bazilevic functions defined with higher order derivatives, Bull. Transilv. Univ. Brasov Ser. III 13(62) (2020), no. 2, 411-422. https://doi.org/10.31926/but.mif.2020.13.62.2.4 
  5. M. K. Aouf and A. M. Lashin, Some remarks on multivalent functions of higher-order derivatives, Bol. Soc. Parana. Mat. (3) 40 (2022), 7 pp. https://doi.org/10.5269/bspm.42646 
  6. M. K. Aouf, A. M. Lashin, and T. Bulboaca, Certain classes of multivalent functions defined with higher-order derivatives, Turkish J. Math. 43 (2019), no. 2, 712-727. https://doi.org/10.3906/mat-1811-26 
  7. M. Arif, K. Ahmad, J.-L. Liu, and J. Soko l, A new class of analytic functions associated with Salagean operator, J. Funct. Spaces 2019, Art. ID 6157394, 8 pp. https://doi.org/10.1155/2019/6157394 
  8. M. Arif, Z. Wang, R. Khan, and S. K. Lee, Coefficient inequalities for Janowski-Sakaguchi type functions associated with conic regions, Hacet. J. Math. Stat. 47 (2018), no. 2, 261-271. 
  9. W. G. Atshan, I. A. Abbas and S. Yal,cin, New concept on fourth-order differential subordination and superordination with some results for multivalent analytic functions, J. Al-Qadisiyah Comp. Sci. Math. 12 (2020), no. 1, 96-107. 
  10. D. Breaz, L.-I. Cotirla, E. Umadevi, and K. R. Karthikeyan, Properties of meromorphic spiral-like functions associated with symmetric functions, J. Funct. Spaces 2022, Art. ID 3444854, 10 pp. https://doi.org/10.1155/2022/3444854 
  11. N. E. Cho, A. Ebadian, S. Bulut, E. A. Adegani, Subordination implications and coefficient estimates for subclasses of starlike functions, Mathematics, 8 (2020), no. 7, 1150. https://doi.org/10.3390/math8071150 
  12. L.-I. Cotirla and K. R. Karthikeyan, Classes of multivalent spirallike functions associated with symmetric regions, Symmetry 14 (2022), no. 8, 1598. https://doi.org/10.3390/sym14081598 
  13. D. J. Hallenbeck and S. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. https://doi.org/10.2307/2040127 
  14. R. W. Ibrahim, On a Janowski formula based on a generalized differential operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 69 (2020), no. 2, 1320-1328. 
  15. R. Kargar, A. Ebadian, and J. Sokol, Radius problems for some subclasses of analytic functions, Complex Anal. Oper. Theory 11 (2017), no. 7, 1639-1649. https://doi.org/10.1007/s11785-016-0584-x 
  16. K. R. Karthikeyan, N. E. Cho and G. Murugusundaramoorthy, On classes of non-Caratheodory functions associated with a family of functions starlike in the direction of the real axis, Axioms 12 (2023), no. 1, Art. ID 24. https://doi.org/10.3390/axioms12010024 
  17. K. R. Karthikeyan, S. Lakshmi, S. Varadharajan, D. Mohankumar and E. Umadevi, Starlike functions of complex order with respect to symmetric points defined using higher order derivatives, Fractal Fract. 6 (2022), Art. ID 116. https://doi.org/10.3390/fractalfract6020116 
  18. K. R. Karthikeyan, G. Murugusundaramoorthy and T. Bulboaca, Properties of λ-pseudo-starlike functions of complex order defined by subordination, Axioms 10 (2021), no. 2, Art. ID 86. https://doi.org/10.3390/axioms10020086 
  19. K. R. Karthikeyan, K. Srinivasan, and K. Ramachandran, On a class of multivalent starlike functions with a bounded positive real part, Palest. J. Math. 5 (2016), no. 1, 59-64. 
  20. O. S. Kwon, Y. J. Sim, N. E. Cho, and H. M. Srivastava, Some radius problems related to a certain subclass of analytic functions, Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 7, 1133-1144. https://doi.org/10.1007/s10114-014-3100-0 
  21. A. M. Y. Lashin and F. Z. El-Emam, On certain classes of multivalent analytic functions defined with higher-order derivatives, Mathematics 11, (2023), no. 1, Art. ID 83. 
  22. S. Li, H. Tang, L. Ma, and X.-M. Niu, Coefficient estimates for the subclasses of analytic functions and bi-univalent functions associated with the strip domain, J. Math. Res. Appl. 37 (2017), no. 5, 550-562. 
  23. H. Mahzoon and J. Sokol, On coefficients of a certain subclass of starlike and bi-starlike functions, Kyungpook Math. J. 61 (2021), no. 3, 513-522. https://doi.org/10.5666/KMJ.2021.61.3.513 
  24. D. Mohankumar, A. Senguttuvan, K. R. Karthikeyan and R. Ganapathy Raman, Initial coefficient bounds and Fekete-Szego problem of pseudo-Bazilevic functions involving quasi-subordination, Adv. Dyn. Syst. Appl. 16 (2021), no. 2, 767-777. 
  25. K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62 (2011), no. 5, 2209-2217. https://doi.org/10.1016/j.camwa.2011.07.006 
  26. M. Nunokawa, On the theory of multivalent functions, Tsukuba J. Math. 11 (1987), no. 2, 273-286. https://doi.org/10.21099/tkbjm/1496160581 
  27. M. Nunokawa, On properties of non-Caratheodory functions, Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), no. 6, 152-153. http://projecteuclid.org/euclid.pja/1195511750 
  28. T. N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szeg˝o problem for subclasses of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (2006), no. 3, 589-598. https://doi.org/10.4134/BKMS.2006.43.3.589 
  29. Y. J. Sim and O. S. Kwon, Notes on analytic functions with a bounded positive real part, J. Inequal. Appl. 2013, 2013:370, 9 pp. https://doi.org/10.1186/1029-242X-2013-370 
  30. H. M. Srivastava, J. Patel, and G. P. Mohapatra, A certain class of p-valently analytic functions, Math. Comput. Modelling 41 (2005), no. 2-3, 321-334. https://doi.org/10.1016/j.mcm.2003.06.010 
  31. Y. Sun, Y.-P. Jiang, and A. Rasila, Coefficient estimates for certain subclasses of analytic and bi-univalent functions, Filomat 29 (2015), no. 2, 351-360. https://doi.org/10.2298/FIL1502351S 
  32. Y. Sun, Y.-P. Jiang, A. Rasila, and H. M. Srivastava, Integral representations and coefficient estimates for a subclass of meromorphic starlike functions, Complex Anal. Oper. Theory 11 (2017), no. 1, 1-19. https://doi.org/10.1007/s11785-016-0531-x 
  33. Y. Sun, Z.-G. Wang, A. Rasila, and J. Sokol, On a subclass of starlike functions associated with a vertical strip domain, J. Inequal. Appl. 2019, Paper No. 35, 14 pp. https://doi.org/10.1186/s13660-019-1988-8 
  34. H. Tang and G.-T. Deng, New subclasses of analytic functions with respect to symmetric and conjugate points, J. Complex Anal. 2013, Art. ID 578036, 9 pp. https://doi.org/10.1155/2013/578036 
  35. Z. Tu and L. Xiong, Unified solution of Fekete-Szego problem for subclasses of starlike mappings in several complex variables, Math. Slovaca 69 (2019), no. 4, 843-856. https://doi.org/10.1515/ms-2017-0273