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Hipergeometrik Fonksiyonu İçeren Harmonik Tek Değerlikli Fonksiyonların Altsınıflarının Bir Uygulaması

Yıl 2020, Cilt: 10 Sayı: 2, 595 - 607, 30.12.2020

Waggas Galib Atshan Enaam Hadi Abd Sibel Yalcın

https://doi.org/10.37094/adyujsci.680530

Öz


Bu makalenin amacı, hipergeometrik fonksiyonları içeren belirli konvolusyon operatörünü uygulayarak harmonik univalent fonksiyonların çeşitli altsınıfları arasında bağlantılar kurmaktır. Bu tür bağlantılar açık birim disk U da Goodman-Salagean tipli harmonik univalent fonksiyonları ile araştırılmıştır.

Kaynakça

  • [1] Hohlov, Y.E., Convolution operators preserving univalent functions, Ukrainian Mathematical Journal, 37, 220-226, 1985.
  • [2] de Branges, L., A proof of the Bieberbach conjecture, Acta Mathematica, 154, 137- 152, 1985.
  • [3] Ahuja, O.P., Connections between various subclasses of planar harmonic mappings Involving hypergeometric functions , Applied Mathematics and Computation, 198 (1), 305-316, 2008.
  • [4] Carleson, B.C., Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM Journal on Mathematical Analysis, 15, 737-745, 1984.
  • [5] Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39, 1057-1077, 1987.
  • [6] Miller, S., Mocanu, P.T., Univalence of Gaussian and confluent hypergeometric Functions, Proceedings of American Mathematical Society, 110(2), 333-342, 1990.
  • [7] Ruscheweyh, S., Singh, V., On the order of starlikeness of hypergeometric functions, Journal of Mathematical Analysis and Applications, 113, 1-11, 1986.
  • [8] Srivastava, H.M., Manocha, H.L., A Treatise on Generating Functions, Ellis Horwood Limited and John Wiley & Sons, New York, Chichester, Toronto, 1984.
  • [9] Swaminathan, A., Certain Sufficiency conditions on Gaussian hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics, 5(4), Article 83, 1-10, 2004.
  • [10] Ahuja, O.P., Planar harmonic convolution operators generated by hypergeometric functions, Integral Transforms and Special Functions, 18 (3), 165-177, 2007.
  • [11] Clunie, J., Sheil-Small, T., Harmonic univalent functions, Annales Academie Scientiarum Fennice, Series A. I. Mathematica 9, 3-25, 1984.
  • [12] Ahuja, O.P., Planar harmonic univalent and related mappings, Journal of Inequalities in Pure and Applied Mathematics, 6(4) Art. 122, 1-18, 2005.
  • [13] Duren, P., Harmonic Mappings in the plane, Cambridge Tracts in Mathematics, Vol. 156, Cambridge University Press, Cambridge, 2004, ISBN 0-521064121-7.
  • [14] Ahuja, O.P., Jahangiri J.M., Noshiro-type harmonic univalent functions, Scientiae Mathematicae Japonicae, 6(2), 253-259, 2002.
  • [15] Aghalary, R., Goodman-Salagean-Type Harmonic Univalent Functions with Varying Arguments, International Journal of Mathematical Analysis, Vol. 1, no. 22, 1051-1057, 2007.
  • [16] Wang, X.T., Liang, X.Q., Zhang, Y.L., Precise coefficient estimates for close-to- convex harmonic univalent mappings, Journal of Mathematical Analysis and Applications, 263(2), 501-509, 2001.

An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function

Yıl 2020, Cilt: 10 Sayı: 2, 595 - 607, 30.12.2020

Waggas Galib Atshan Enaam Hadi Abd Sibel Yalcın

https://doi.org/10.37094/adyujsci.680530

Öz

The main purpose of this paper is to establish connections between various subclasses of harmonic univalent functions by applying certain convolution operator involving hypergeometric functions. We investigate such connections with Goodman- Salagean-Type harmonic univalent functions in the open unit disc U.

Anahtar Kelimeler

Univalent function uniformly convex linear operator hadamard product

Kaynakça

  • [1] Hohlov, Y.E., Convolution operators preserving univalent functions, Ukrainian Mathematical Journal, 37, 220-226, 1985.
  • [2] de Branges, L., A proof of the Bieberbach conjecture, Acta Mathematica, 154, 137- 152, 1985.
  • [3] Ahuja, O.P., Connections between various subclasses of planar harmonic mappings Involving hypergeometric functions , Applied Mathematics and Computation, 198 (1), 305-316, 2008.
  • [4] Carleson, B.C., Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM Journal on Mathematical Analysis, 15, 737-745, 1984.
  • [5] Owa, S., Srivastava, H.M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39, 1057-1077, 1987.
  • [6] Miller, S., Mocanu, P.T., Univalence of Gaussian and confluent hypergeometric Functions, Proceedings of American Mathematical Society, 110(2), 333-342, 1990.
  • [7] Ruscheweyh, S., Singh, V., On the order of starlikeness of hypergeometric functions, Journal of Mathematical Analysis and Applications, 113, 1-11, 1986.
  • [8] Srivastava, H.M., Manocha, H.L., A Treatise on Generating Functions, Ellis Horwood Limited and John Wiley & Sons, New York, Chichester, Toronto, 1984.
  • [9] Swaminathan, A., Certain Sufficiency conditions on Gaussian hypergeometric functions, Journal of Inequalities in Pure and Applied Mathematics, 5(4), Article 83, 1-10, 2004.
  • [10] Ahuja, O.P., Planar harmonic convolution operators generated by hypergeometric functions, Integral Transforms and Special Functions, 18 (3), 165-177, 2007.
  • [11] Clunie, J., Sheil-Small, T., Harmonic univalent functions, Annales Academie Scientiarum Fennice, Series A. I. Mathematica 9, 3-25, 1984.
  • [12] Ahuja, O.P., Planar harmonic univalent and related mappings, Journal of Inequalities in Pure and Applied Mathematics, 6(4) Art. 122, 1-18, 2005.
  • [13] Duren, P., Harmonic Mappings in the plane, Cambridge Tracts in Mathematics, Vol. 156, Cambridge University Press, Cambridge, 2004, ISBN 0-521064121-7.
  • [14] Ahuja, O.P., Jahangiri J.M., Noshiro-type harmonic univalent functions, Scientiae Mathematicae Japonicae, 6(2), 253-259, 2002.
  • [15] Aghalary, R., Goodman-Salagean-Type Harmonic Univalent Functions with Varying Arguments, International Journal of Mathematical Analysis, Vol. 1, no. 22, 1051-1057, 2007.
  • [16] Wang, X.T., Liang, X.Q., Zhang, Y.L., Precise coefficient estimates for close-to- convex harmonic univalent mappings, Journal of Mathematical Analysis and Applications, 263(2), 501-509, 2001.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Waggas Galib Atshan 0000-0002-7033-8993

Enaam Hadi Abd Bu kişi benim 0000-0003-3580-8379

Sibel Yalcın 0000-0002-0243-8263

Yayımlanma Tarihi 30 Aralık 2020
Gönderilme Tarihi 27 Ocak 2020
Kabul Tarihi 11 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

Kaynak Göster

APA Atshan, W. G., Abd, E. H., & Yalcın, S. (2020). An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function. Adıyaman University Journal of Science, 10(2), 595-607. https://doi.org/10.37094/adyujsci.680530
AMA Atshan WG, Abd EH, Yalcın S. An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function. ADYU J SCI. Aralık 2020;10(2):595-607. doi:10.37094/adyujsci.680530
Chicago Atshan, Waggas Galib, Enaam Hadi Abd, ve Sibel Yalcın. “An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function”. Adıyaman University Journal of Science 10, sy. 2 (Aralık 2020): 595-607. https://doi.org/10.37094/adyujsci.680530.
EndNote Atshan WG, Abd EH, Yalcın S (01 Aralık 2020) An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function. Adıyaman University Journal of Science 10 2 595–607.
IEEE W. G. Atshan, E. H. Abd, ve S. Yalcın, “An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function”, ADYU J SCI, c. 10, sy. 2, ss. 595–607, 2020, doi: 10.37094/adyujsci.680530.
ISNAD Atshan, Waggas Galib vd. “An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function”. Adıyaman University Journal of Science 10/2 (Aralık 2020), 595-607. https://doi.org/10.37094/adyujsci.680530.
JAMA Atshan WG, Abd EH, Yalcın S. An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function. ADYU J SCI. 2020;10:595–607.
MLA Atshan, Waggas Galib vd. “An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function”. Adıyaman University Journal of Science, c. 10, sy. 2, 2020, ss. 595-07, doi:10.37094/adyujsci.680530.
Vancouver Atshan WG, Abd EH, Yalcın S. An Application of Subclasses of Harmonic Univalent Functions Involving Hypergeometric Function. ADYU J SCI. 2020;10(2):595-607.
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