Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

D. Vamshee Krishna[1]; B. Venkateswarlu[1]; T. RamReddy[2]

  • [1] Department of Mathematics GIT, GITAM University Visakhapatnam- 530 045, A.P., India.
  • [2] Department of Mathematics, Kakatiya University, Warangal- 506 009, A.P., India.

Annales mathématiques Blaise Pascal (2014)

  • Volume: 21, Issue: 2, page 39-56
  • ISSN: 1259-1734

Abstract

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The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the k t h root transform f ( z k ) 1 k of normalized analytic function f ( z ) belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.

How to cite

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Vamshee Krishna, D., Venkateswarlu, B., and RamReddy, T.. "Coefficient inequality for transforms of parabolic starlike and uniformly convex functions." Annales mathématiques Blaise Pascal 21.2 (2014): 39-56. <http://eudml.org/doc/275600>.

@article{VamsheeKrishna2014,
abstract = {The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the $k^\{th\}$ root transform $\left[ f(z ^k ) \right] ^\{\frac\{1\}\{k\}\}$ of normalized analytic function $f(z)$ belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.},
affiliation = {Department of Mathematics GIT, GITAM University Visakhapatnam- 530 045, A.P., India.; Department of Mathematics GIT, GITAM University Visakhapatnam- 530 045, A.P., India.; Department of Mathematics, Kakatiya University, Warangal- 506 009, A.P., India.},
author = {Vamshee Krishna, D., Venkateswarlu, B., RamReddy, T.},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Analytic function; parabolic starlike and uniformly convex functions; upper bound; second Hankel functional; positive real function; Toeplitz determinants; parabolic star-like functions; uniformly convex functions},
language = {eng},
month = {7},
number = {2},
pages = {39-56},
publisher = {Annales mathématiques Blaise Pascal},
title = {Coefficient inequality for transforms of parabolic starlike and uniformly convex functions},
url = {http://eudml.org/doc/275600},
volume = {21},
year = {2014},
}

TY - JOUR
AU - Vamshee Krishna, D.
AU - Venkateswarlu, B.
AU - RamReddy, T.
TI - Coefficient inequality for transforms of parabolic starlike and uniformly convex functions
JO - Annales mathématiques Blaise Pascal
DA - 2014/7//
PB - Annales mathématiques Blaise Pascal
VL - 21
IS - 2
SP - 39
EP - 56
AB - The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the $k^{th}$ root transform $\left[ f(z ^k ) \right] ^{\frac{1}{k}}$ of normalized analytic function $f(z)$ belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.
LA - eng
KW - Analytic function; parabolic starlike and uniformly convex functions; upper bound; second Hankel functional; positive real function; Toeplitz determinants; parabolic star-like functions; uniformly convex functions
UR - http://eudml.org/doc/275600
ER -

References

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