Research Article
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Certain Classes of Analytic Functions Associated with Conic Domains

Year 2018, Issue: 24, 20 - 34, 14.08.2018
https://izlik.org/JA58GX64PP

Abstract

In this paper, we define new subclasses of k-uniformly Janowski starlike and k-uniformly
Janowski convex functions associated with m-symmetric points. The integral representations, convolution
properties and sufficient conditions for the functions belong to this class are investigated.

References

  • [1] R. Chand and P. Singh, On certain schlicht mapping, Ind. J. Pure App. Math. 10 (1979), 1167-1174.
  • [2] W. Janowski, Some external problem for certain families of analytic functions I, Ann. Polon. Math., 28 (1973), 298-326.
  • [3] S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105(1999), 327-336.
  • [4] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (2000), 647-657.
  • [5] K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62 (2011), 2209-2217.
  • [6] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan. 11 (1959), 72- 75.
  • [7] M. Arif, K. I. Noor and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. (2012), ID 790689, 11 pages.
  • [8] K. I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation with respect to symmetrical points, J. Math. Ineq. 3 (2) (2009), 267-276.
  • [9] T. N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szego problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3) (2006), 589-598.
  • [10] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28 (2013), 143-154.
  • [11] S. Shams, S. R. Kulkarni, and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55 (2004), 2959–2961.
  • [12] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
  • [13] S. S. Miller and P. T Mocanu, Subordinates of differential superordinations, Complex Variables, 48 (10) (2003), 815–826.
  • [14] T. Bulboac a, Differential Subordinations and Superordinations, Recent Results, House of Scientic Book Publ, Cluj-Napoca, 2005.
  • [15] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstratio Math., 42 (1) (2009), 109–122.
  • [16] R. N. Das and P. Singh, On subclasses of Schlicht mappings. Ind. J. Pure. App. Math. 8(1977), 864-872.

Year 2018, Issue: 24, 20 - 34, 14.08.2018
https://izlik.org/JA58GX64PP

Abstract

References

  • [1] R. Chand and P. Singh, On certain schlicht mapping, Ind. J. Pure App. Math. 10 (1979), 1167-1174.
  • [2] W. Janowski, Some external problem for certain families of analytic functions I, Ann. Polon. Math., 28 (1973), 298-326.
  • [3] S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105(1999), 327-336.
  • [4] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (2000), 647-657.
  • [5] K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62 (2011), 2209-2217.
  • [6] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan. 11 (1959), 72- 75.
  • [7] M. Arif, K. I. Noor and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. (2012), ID 790689, 11 pages.
  • [8] K. I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation with respect to symmetrical points, J. Math. Ineq. 3 (2) (2009), 267-276.
  • [9] T. N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szego problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3) (2006), 589-598.
  • [10] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28 (2013), 143-154.
  • [11] S. Shams, S. R. Kulkarni, and J. M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55 (2004), 2959–2961.
  • [12] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
  • [13] S. S. Miller and P. T Mocanu, Subordinates of differential superordinations, Complex Variables, 48 (10) (2003), 815–826.
  • [14] T. Bulboac a, Differential Subordinations and Superordinations, Recent Results, House of Scientic Book Publ, Cluj-Napoca, 2005.
  • [15] A. Aral and V. Gupta, On q-Baskakov type operators, Demonstratio Math., 42 (1) (2009), 109–122.
  • [16] R. N. Das and P. Singh, On subclasses of Schlicht mappings. Ind. J. Pure. App. Math. 8(1977), 864-872.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Nasir Khan This is me

Submission Date March 20, 2018
Publication Date August 14, 2018
IZ https://izlik.org/JA58GX64PP
Published in Issue Year 2018 Issue: 24

Cite

APA Khan, N. (2018). Certain Classes of Analytic Functions Associated with Conic Domains. Journal of New Theory, 24, 20-34. https://izlik.org/JA58GX64PP
AMA 1.Khan N. Certain Classes of Analytic Functions Associated with Conic Domains. JNT. 2018;(24):20-34. https://izlik.org/JA58GX64PP
Chicago Khan, Nasir. 2018. “Certain Classes of Analytic Functions Associated With Conic Domains”. Journal of New Theory, nos. 24: 20-34. https://izlik.org/JA58GX64PP.
EndNote Khan N (August 1, 2018) Certain Classes of Analytic Functions Associated with Conic Domains. Journal of New Theory 24 20–34.
IEEE [1]N. Khan, “Certain Classes of Analytic Functions Associated with Conic Domains”, JNT, no. 24, pp. 20–34, Aug. 2018, [Online]. Available: https://izlik.org/JA58GX64PP
ISNAD Khan, Nasir. “Certain Classes of Analytic Functions Associated With Conic Domains”. Journal of New Theory. 24 (August 1, 2018): 20-34. https://izlik.org/JA58GX64PP.
JAMA 1.Khan N. Certain Classes of Analytic Functions Associated with Conic Domains. JNT. 2018;:20–34.
MLA Khan, Nasir. “Certain Classes of Analytic Functions Associated With Conic Domains”. Journal of New Theory, no. 24, Aug. 2018, pp. 20-34, https://izlik.org/JA58GX64PP.
Vancouver 1.Nasir Khan. Certain Classes of Analytic Functions Associated with Conic Domains. JNT [Internet]. 2018 Aug. 1;(24):20-34. Available from: https://izlik.org/JA58GX64PP


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