Year 2020, Volume 49 , Issue 4, Pages 1346 - 1354 2020-08-06

A new subclass of analytic functions

Hesam MAHZON [1] , Janusz SOKOL [2]


In the present paper, we introduce a class $\mathcal{B}_\theta(\alpha,\beta)$ of functions, analytic in $|z|<1$, such that $f(0)=0$, $f'(0)=1$ and
\[\alpha< Re\left(f'(z)+\frac{1+e^{i\theta}}{2}zf''(z)\right)<\beta\quad (|z|<1),\]
where $\theta\in(-\pi,\pi]$, $0\leq\alpha<1$ and $\beta>1$. Integral representation, differential subordination results and coefficient estimates are considered. Also Fekete-Szegö coefficient functional associated with the $k$--th root transform $[f(z^k)]^{1/k}$ for functions in the class $\mathcal{B}_\theta(\alpha,\beta)$ is investigated.
analytic functions, univalent functions, Carathéodory functions, differential subordination, Fekete-Szegö inequality
  • [1] R.M. Ali, S.K. Lee, V. Ravichandran and S. Supramanian, The Fekete-Szegö coefficient functional for transforms of analytic functions, Bull. Iranian Math. Soc. 35, 119–142, 2009.
  • [2] P.N. Chichra, New subclasses of the class of close-to-convex functions, Proc. Amer. Math. Soc. 62, 37–43, 1977.
  • [3] D.J. Hallenbeck and St. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52, 191–195, 1975.
  • [4] R. Kargar, A. Ebadian, J. Sokół, On subordination of some analytic functions, Sib. Math. J. 57, 599–605, 2016.
  • [5] R. Kargar, A. Ebadian and J. Sokół, Radius problems for some subclasses of analytic functions, Complex Anal. Oper. Theory 11, 1639–1649, 2017.
  • [6] R. Kargar, A. Ebadian and J. Sokół, On Booth lemniscate and starlike functions, Anal. Math. Phys. 9, 143–154, 2019.
  • [7] F.R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20, 8–12, 1969.
  • [8] K. Kuroki and S. Owa, Notes on New Class for Certain Analytic Functions, RIMS Kokyuroku Kyoto Univ. 1772, 21–25, 2011.
  • [9] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc. 49, 109–115, 1975.
  • [10] St. Ruscheweyh and T. Sheil-Small, Hadamard products of schlicht functions and the Polya-Schoenberg conjecture, Comment. Math. Helv. 48, 119–135, 1973.
  • [11] W. Rogosinski, On the coefficients of subordinate functions, Proc. London Math. Soc. 48, 48–82, 1943.
  • [12] H. Silverman, A class of bounded starlike functions, Internat. J. Math. Math. Sci. 17, 249–252, 1994.
  • [13] H. Silverman and E.M. Silvia, Characterizations for subclasses of univalent functions, Math. Japan. 50, 103–109, 1999.
  • [14] R. Singh and S. Singh, Convolutions properties of a class of starlike functions, Proc. Amer. Math. Soc. 106, 145–152, 1989.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-3167-4134
Author: Hesam MAHZON
Institution: Islamic Azad University
Country: Iran


Orcid: 0000-0003-1204-2286
Author: Janusz SOKOL (Primary Author)
Institution: University of Rzeszów
Country: Poland


Dates

Publication Date : August 6, 2020

Bibtex @research article { hujms549313, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1346 - 1354}, doi = {10.15672/hujms.549313}, title = {A new subclass of analytic functions}, key = {cite}, author = {Mahzon, Hesam and Sokol, Janusz} }
APA Mahzon, H , Sokol, J . (2020). A new subclass of analytic functions . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1346-1354 . DOI: 10.15672/hujms.549313
MLA Mahzon, H , Sokol, J . "A new subclass of analytic functions" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1346-1354 <https://dergipark.org.tr/en/pub/hujms/issue/56305/549313>
Chicago Mahzon, H , Sokol, J . "A new subclass of analytic functions". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1346-1354
RIS TY - JOUR T1 - A new subclass of analytic functions AU - Hesam Mahzon , Janusz Sokol Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.549313 DO - 10.15672/hujms.549313 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1346 EP - 1354 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.549313 UR - https://doi.org/10.15672/hujms.549313 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics A new subclass of analytic functions %A Hesam Mahzon , Janusz Sokol %T A new subclass of analytic functions %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.549313 %U 10.15672/hujms.549313
ISNAD Mahzon, Hesam , Sokol, Janusz . "A new subclass of analytic functions". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1346-1354 . https://doi.org/10.15672/hujms.549313
AMA Mahzon H , Sokol J . A new subclass of analytic functions. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1346-1354.
Vancouver Mahzon H , Sokol J . A new subclass of analytic functions. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1346-1354.