Research Article
BibTex RIS Cite

Holomorfik fonksiyonlar için Carathèodory eşitsizliğinin genellemesi

Year 2017, Volume: 21 Issue: 6, 1254 - 1257, 01.12.2017
https://doi.org/10.16984/saufenbilder.337277

Abstract

Bu makalede,
Carathèodory eşitsizliğinin sonuçları genelleştirilmiştir. C. T. Rajagopal
 eşitsizliğini,  fonksiyonun
sıfırlarını da göz önüne alarak daha da güçlendirmiştir. Biz
 fonksiyonun hem
sıfırlarını hem de kutuplarını göz önünde bulundurarak,
 ve  eşitsizlikleri için
daha genel sonuçlar elde edeceğiz.

References

  • [1] V.N. Dubinin, On application of conformal maps to inequalities for rational function, Izv. Math. 66, 285-297, 2002. [2] G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, 2nd ed. [in Russian], Moscow, 1966. [3] L.S. Hahn and B. Epstein, Clasical Complex Analysis, Jones and Bartlett Publishers International, 1996. [4] G. Kresin and V. Maz'ya , Sharp real-part theorems. A unified approach, Translated from the Russian and edited by T. Shaposhnikova. Lecture Notes in Mathematics, 1903. Springer, Berlin, 2007. [5] C.T. Rajagopal, Carathèodory's inequality and allied results, Math. Student, 9, 73-77, 1941. [6] E. Lindelöf, Mèmoire sur certaines inègalitès dans la thèorie des fonctions monogènes et sur quelques proprièt´es nouvelles de ces fonctions dans le voisinage d'un point singulier essentiel, Acta Soc. Sci. Fennicae, 35, 1-35, 1908.

The generalizations of the Carathèodory Inequality for the holomorphic functions

Year 2017, Volume: 21 Issue: 6, 1254 - 1257, 01.12.2017
https://doi.org/10.16984/saufenbilder.337277

Abstract

In this paper, the
results of the Carathèodory inequality have been generalized. C. T. Rajagopal
further strengthened the inequality
 by considering the
zeros of the function
. We will obtain more general results for the inequalities  and  by considering both
the zeros and the poles of the function
.

References

  • [1] V.N. Dubinin, On application of conformal maps to inequalities for rational function, Izv. Math. 66, 285-297, 2002. [2] G.M. Goluzin, Geometric Theory of Functions of a Complex Variable, 2nd ed. [in Russian], Moscow, 1966. [3] L.S. Hahn and B. Epstein, Clasical Complex Analysis, Jones and Bartlett Publishers International, 1996. [4] G. Kresin and V. Maz'ya , Sharp real-part theorems. A unified approach, Translated from the Russian and edited by T. Shaposhnikova. Lecture Notes in Mathematics, 1903. Springer, Berlin, 2007. [5] C.T. Rajagopal, Carathèodory's inequality and allied results, Math. Student, 9, 73-77, 1941. [6] E. Lindelöf, Mèmoire sur certaines inègalitès dans la thèorie des fonctions monogènes et sur quelques proprièt´es nouvelles de ces fonctions dans le voisinage d'un point singulier essentiel, Acta Soc. Sci. Fennicae, 35, 1-35, 1908.
There are 1 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Bülent Nafi Örnek

Tuğba Akyel This is me

Publication Date December 1, 2017
Submission Date September 8, 2017
Acceptance Date June 15, 2017
Published in Issue Year 2017 Volume: 21 Issue: 6

Cite

APA Örnek, B. N., & Akyel, T. (2017). The generalizations of the Carathèodory Inequality for the holomorphic functions. Sakarya University Journal of Science, 21(6), 1254-1257. https://doi.org/10.16984/saufenbilder.337277
AMA Örnek BN, Akyel T. The generalizations of the Carathèodory Inequality for the holomorphic functions. SAUJS. December 2017;21(6):1254-1257. doi:10.16984/saufenbilder.337277
Chicago Örnek, Bülent Nafi, and Tuğba Akyel. “The Generalizations of the Carathèodory Inequality for the Holomorphic Functions”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1254-57. https://doi.org/10.16984/saufenbilder.337277.
EndNote Örnek BN, Akyel T (December 1, 2017) The generalizations of the Carathèodory Inequality for the holomorphic functions. Sakarya University Journal of Science 21 6 1254–1257.
IEEE B. N. Örnek and T. Akyel, “The generalizations of the Carathèodory Inequality for the holomorphic functions”, SAUJS, vol. 21, no. 6, pp. 1254–1257, 2017, doi: 10.16984/saufenbilder.337277.
ISNAD Örnek, Bülent Nafi - Akyel, Tuğba. “The Generalizations of the Carathèodory Inequality for the Holomorphic Functions”. Sakarya University Journal of Science 21/6 (December 2017), 1254-1257. https://doi.org/10.16984/saufenbilder.337277.
JAMA Örnek BN, Akyel T. The generalizations of the Carathèodory Inequality for the holomorphic functions. SAUJS. 2017;21:1254–1257.
MLA Örnek, Bülent Nafi and Tuğba Akyel. “The Generalizations of the Carathèodory Inequality for the Holomorphic Functions”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1254-7, doi:10.16984/saufenbilder.337277.
Vancouver Örnek BN, Akyel T. The generalizations of the Carathèodory Inequality for the holomorphic functions. SAUJS. 2017;21(6):1254-7.