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Year 2020, Volume: 49 Issue: 2, 716 - 726, 02.04.2020
https://doi.org/10.15672/hujms.588741

Abstract

References

  • [1] M. Arif, K.I. Noor, and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. 2012, 790689, 2012.
  • [2] R. Chand and P. Singh, On certain schlicht mapping, Indian J. Pure App. Math. 10, 1167–1174, 1979.
  • [3] W. Janowski, Some extremal problem for certain families of analytic functions, Ann. Polon. Math. 28 (3), 298–326, 1973.
  • [4] S. Kanas and A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105, 327–336, 1999.
  • [5] S. Kanas and A. Wiśniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (4), 647–657, 2000.
  • [6] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28, 143–154, 2013.
  • [7] S.S. Miller and P.T. Mocanu, Differential Subordinations, Theory and Applications, in: Series of Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York, 2000.
  • [8] K.I. Noor and S.N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62, 2209–2217, 2011.
  • [9] K.I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation eith respect to symmetrical points, J. Math. Ineq. 2 (3), 267–276, 2009.
  • [10] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11, 72–75, 1959.
  • [11] S. Shams, S.R. Kulkarni, and J.M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55, 2959–2961, 2004.
  • [12] T.N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szegö problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3), 589–598, 2006.
  • [13] H. Silverman, Univalent functions with negative coefficients, Proc. Amr. Math. Soc. 51, 109–116, 1975.
  • [14] J. Sokół, Some remarks on the class of functions starlike with respect to symmetric points, Folia Sci. Univ. Tech. Resov. 73, 79–91, 1990.

On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points

Year 2020, Volume: 49 Issue: 2, 716 - 726, 02.04.2020
https://doi.org/10.15672/hujms.588741

Abstract

In this paper, we define new subclasses of $k$-uniformly Janowski starlike and $k$-uniformly Janowski convex functions associated with $t$-symmetric points. The integral representations, convolution properties and coefficient bounds for these classes are studied.

References

  • [1] M. Arif, K.I. Noor, and R. Khan, On subclasses of analytic functions with respect to symmetrical points, Abst. Appl. Anal. 2012, 790689, 2012.
  • [2] R. Chand and P. Singh, On certain schlicht mapping, Indian J. Pure App. Math. 10, 1167–1174, 1979.
  • [3] W. Janowski, Some extremal problem for certain families of analytic functions, Ann. Polon. Math. 28 (3), 298–326, 1973.
  • [4] S. Kanas and A. Wiśniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105, 327–336, 1999.
  • [5] S. Kanas and A. Wiśniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pure. Appl. 45 (4), 647–657, 2000.
  • [6] O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetric points, Commun. Korean Math. Soc. 28, 143–154, 2013.
  • [7] S.S. Miller and P.T. Mocanu, Differential Subordinations, Theory and Applications, in: Series of Monographs and Textbooks in Pure and Applied Mathematics 225, Marcel Dekker Inc., New York, 2000.
  • [8] K.I. Noor and S.N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62, 2209–2217, 2011.
  • [9] K.I. Noor and S. Mustafa, Some classes of analytic functions related with functions of bounded radius rotation eith respect to symmetrical points, J. Math. Ineq. 2 (3), 267–276, 2009.
  • [10] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11, 72–75, 1959.
  • [11] S. Shams, S.R. Kulkarni, and J.M. Jahangiri, Classes of uniformly starlike and convex functions, Int. J. Math. Math. Sci. 55, 2959–2961, 2004.
  • [12] T.N. Shanmugam, C. Ramachandran, and V. Ravichandran, Fekete-Szegö problem for subclass of starlike functions with respect to symmetric points, Bull. Korean Math. Soc. 43 (3), 589–598, 2006.
  • [13] H. Silverman, Univalent functions with negative coefficients, Proc. Amr. Math. Soc. 51, 109–116, 1975.
  • [14] J. Sokół, Some remarks on the class of functions starlike with respect to symmetric points, Folia Sci. Univ. Tech. Resov. 73, 79–91, 1990.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Khalida Inayat Noor This is me 0000-0002-5000-3870

Nasir Khan This is me 0000-0002-5486-3501

Muhammad Arif This is me 0000-0003-1484-7643

Janusz Sokol 0000-0003-1204-2286

Publication Date April 2, 2020
Published in Issue Year 2020 Volume: 49 Issue: 2

Cite

APA Noor, K. I., Khan, N., Arif, M., Sokol, J. (2020). On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points. Hacettepe Journal of Mathematics and Statistics, 49(2), 716-726. https://doi.org/10.15672/hujms.588741
AMA Noor KI, Khan N, Arif M, Sokol J. On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points. Hacettepe Journal of Mathematics and Statistics. April 2020;49(2):716-726. doi:10.15672/hujms.588741
Chicago Noor, Khalida Inayat, Nasir Khan, Muhammad Arif, and Janusz Sokol. “On Some Subclasses $k$-Uniformly Janowski Starlike and Convex Functions Associated With $t$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics 49, no. 2 (April 2020): 716-26. https://doi.org/10.15672/hujms.588741.
EndNote Noor KI, Khan N, Arif M, Sokol J (April 1, 2020) On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points. Hacettepe Journal of Mathematics and Statistics 49 2 716–726.
IEEE K. I. Noor, N. Khan, M. Arif, and J. Sokol, “On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, pp. 716–726, 2020, doi: 10.15672/hujms.588741.
ISNAD Noor, Khalida Inayat et al. “On Some Subclasses $k$-Uniformly Janowski Starlike and Convex Functions Associated With $t$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics 49/2 (April 2020), 716-726. https://doi.org/10.15672/hujms.588741.
JAMA Noor KI, Khan N, Arif M, Sokol J. On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points. Hacettepe Journal of Mathematics and Statistics. 2020;49:716–726.
MLA Noor, Khalida Inayat et al. “On Some Subclasses $k$-Uniformly Janowski Starlike and Convex Functions Associated With $t$-Symmetric Points”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 2, 2020, pp. 716-2, doi:10.15672/hujms.588741.
Vancouver Noor KI, Khan N, Arif M, Sokol J. On some subclasses $k$-uniformly Janowski starlike and convex functions associated with $t$-symmetric points. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):716-2.