JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SHARPENED FORMS OF THE SCHWARZ LEMMA ON THE BOUNDARY
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SHARPENED FORMS OF THE SCHWARZ LEMMA ON THE BOUNDARY
Ornek, Bulent Nafi;
  PDF(new window)
 Abstract
In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.
 Keywords
Schwarz lemma on the boundary;holomorphic function;angular limit and derivative;Julia-Wolff-Lemma;
 Language
English
 Cited by
1.
THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT,;

한국수학교육학회지시리즈B:순수및응용수학, 2014. vol.21. 3, pp.219-227 crossref(new window)
2.
INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION,;

대한수학회논문집, 2014. vol.29. 3, pp.439-449 crossref(new window)
3.
CARATHÉODORY'S INEQUALITY ON THE BOUNDARY,;

한국수학교육학회지시리즈B:순수및응용수학, 2015. vol.22. 2, pp.169-178 crossref(new window)
4.
A SHARP SCHWARZ LEMMA AT THE BOUNDARY,;;

한국수학교육학회지시리즈B:순수및응용수학, 2015. vol.22. 3, pp.263-273 crossref(new window)
5.
AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY,;;

한국수학교육학회지시리즈B:순수및응용수학, 2016. vol.23. 1, pp.61-72 crossref(new window)
6.
INEQUALITIES FOR THE ANGULAR DERIVATIVES OF CERTAIN CLASSES OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISC,;

대한수학회보, 2016. vol.53. 2, pp.325-334 crossref(new window)
7.
A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY,;

대한수학회논문집, 2016. vol.31. 3, pp.533-547 crossref(new window)
1.
Bounded Holomorphic Functions Covering No Concentric Circles, Journal of Mathematical Sciences, 2015, 207, 6, 825  crossref(new windwow)
2.
Schwarz lemma at the boundary of the unit polydisk in ℂ n, Science China Mathematics, 2015, 58, 8, 1639  crossref(new windwow)
3.
A SHARP SCHWARZ LEMMA AT THE BOUNDARY, The Pure and Applied Mathematics, 2015, 22, 3, 263  crossref(new windwow)
4.
Sharpened forms of the generalized Schwarz inequality on the boundary, Proceedings - Mathematical Sciences, 2016, 126, 1, 69  crossref(new windwow)
5.
THE SCHWARZ LEMMA AND ITS APPLICATION AT A BOUNDARY POINT, The Pure and Applied Mathematics, 2014, 21, 3, 219  crossref(new windwow)
6.
INEQUALITIES FOR THE NON-TANGENTIAL DERIVATIVE AT THE BOUNDARY FOR HOLOMORPHIC FUNCTION, Communications of the Korean Mathematical Society, 2014, 29, 3, 439  crossref(new windwow)
7.
CARATHÉODORY'S INEQUALITY ON THE BOUNDARY, The Pure and Applied Mathematics, 2015, 22, 2, 169  crossref(new windwow)
8.
INEQUALITIES FOR THE ANGULAR DERIVATIVES OF CERTAIN CLASSES OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISC, Bulletin of the Korean Mathematical Society, 2016, 53, 2, 325  crossref(new windwow)
9.
A SHARP CARATHÉODORY'S INEQUALITY ON THE BOUNDARY, Communications of the Korean Mathematical Society, 2016, 31, 3, 533  crossref(new windwow)
10.
AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY, The Pure and Applied Mathematics, 2016, 23, 1, 61  crossref(new windwow)
 References
1.
V. N. Dubinin, On the Schwarz inequality on the boundary for functions regular in the disk, J. Math. Sci. (N. Y.) 122 (2004), no. 6, 3623-3629. crossref(new window)

2.
G. M. Golusin, Geometric Theory of Functions of Complex Variable, 2nd edn., Moscow 1966.

3.
A. I. Markushevich, Theory of Functions of a Complex Variable. Volume I, 1965.

4.
R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Math. Soc. 128 (2000), no. 12, 3513-3517. crossref(new window)

5.
Ch. Pommerenke, Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.