حول بعض الأصناف المعممة للدوال المتعددة التكافؤ ذات المعاملات السالبة المعرفة بواسطة مؤثر خطي
الكلمات المفتاحية:
الدوال التحليلية، الدوال المتعددة التكافؤ، المؤثر الخطي، المعاملات السالبةالملخص
تتناول هذه الورقة دراسة بعض الأصناف المعممة من الدوال التحليلية المتعددة التكافؤ ذات المعاملات السالبة والمعرَّفة بواسطة مؤثر خطي. حيث يتم اشتقاق تقديرات حادة لمعاملات هذه الدوال، وإثبات نتائج تتعلق بتشوهها الهندسي ضمن الأصناف المقترحة. كما يتم تحديد أنصاف أقطار التحدب القريب، والنجومية، والتحدب المرتبطة بهذه الأصناف. وتُعد النتائج المتحصل عليها امتدادًا وتوحيدًا لعدد من الأعمال السابقة في نظرية الدوال المتعددة التكافؤ، كما تقدم رؤى جديدة حول السلوك الهندسي للدوال المعرفة بواسطة مؤثرات خطية
المراجع
A. Catas, On certain classes of p-valent functions defined by multiplitier
Transformations, in Proc. Book of the Intenational Symposium on Geome-
tric Functions Theory and Applications, Istanbul, Turkey, (August 2007),
-250.
A. R. Ahmed and Z. H. Omer, About New class 0f Univalent starlike
functions involving Ruscheweyh operator, Sebha University., Vol.2(2021),
-156.
A. R. Ahmed, Some Applications of Catas Operator to P-valent Starlike
functions, Surman Journal., Vol6, (2024), 401-410.
A. R. S. Juma and F. S. Aziz, Some subordination and superordination
results for the generalized hypergeometric function associated with
Ruscheweyh derivative, Le Matematiche, Vol. LXIX (2014)-Fasc. II, 17-29.
A. W. Goodman, On the Schwarz-Christoffel transformation and p-valent
functions, Trans. Amer. Math. Soc., 68 (1950), 204-223
A. W. Goodman, Univalent functions, Vol. I, II, Mariner, Tampa, Florida
(1983).
A. W. Goodman, Univalent functions, vol.II, Polygonal Publishing House,
Washington, N. J., 1983.
D. A. Patel and N. K. Thakare, On convex hulls and extreme points of
p-valent starlike and convex classes with applications, Bull. Soc. Sci.
Math.Roum., 27 (1983), 145-160.
D. K. Thomas, N. Tuneski and A. Vasudevarao, Univalent functions: a
Primer (Vol. 69). Walter de Gruyter GmbH and Co KG, (2018).
E. A. Elrifai, H. E. Darwish and A. R. Ahmed, Some Applications of Sriv-
astava-Attiya Operator to p-Valent Starlike Functions, Applied Mathematics
Letters. 25(2010).
E. A. Elrifai, H. E. Darwish and A. R. Ahmed, On certain subclasses of
Meromorphic functions associated with certain differential operators,
Applied Mathematics Letters. 2 (2011) 1225-1235.
H. Orhan and H. Kiziltunc, A generalization on subfamily of p-valent
functions with negative coefficients, Appl. Math. Comput., 155(2004),
- 530.
I. S. Jack, "Functions starlike and convex of order α,”Journal of the
London Mathematical Society, vol. 3, 1971, 469-474.
J. L. Liu and H. M. Srivastava, Classes of meromorphically multivalent
Functions associated with the generalized hypergeometric function, Math.
Comput. Modelling, 39(2004), 21-34.
J. W. Alexander, Functions which map the interior of the unit circle upon
Simple regions, Ann. Math., 17(1915-1916),12-22.
M. Acu, S. Owa, Note on a class of strlike functions, 2007, 1-10.
M. K. Aouf, "On a class of p-valent close-to-convex functions of order β
and α,” International Journal of Mathematics and Mathematical Sciences,
vol. 11, 1988, 259-266.
P. Eenigenburg, S. Miller, P. Mocanu and M. Reade, "On a Biriot-Bouquet
differential subordination," General Inequalities 3, International series of
Numerical Mathematics, Vol. 64, BirkhauserVerlag Basel (1983), 339-348.
P. L. Duren, Univalent functions, Grundlehren der Mathematischen
Wissenschaften, 259, Springer-Verlag, New York, Berlin, Heidelberg and
Tokyo, (1983).
R. J. Libera, "Some radius of convexity problems,”Duke Mathematical
Journal, vol. 31, no. 1, 1964, 143-158.
R. J. Libera, some classes of regular univalent functions, Proc. Amer.
Math. Soc., 16(1965), 653-758.
R. J. Libera, "Some class of regular univalent functions,”Proceeding of
the American Mathematical Society, vol. 16, 1978, 755-758.
R. Yamakawa, “Certain Subclasses of p-Valently Starlike Functions with
Negative Coefficients,” In: H. M. Srivas- tava and S. Owa, Eds., Current
Topics in Analytic Function Theory, World Scientific Publishing Company,
Singapore, 1992, 393-402.
S. D. Bernardi, "Convex and starlike univalent functions,”Transactions
of the American Mathematical Society, vol. 135, pp. 429-446, 1969.
S. Ruscheweyh., New criteria for univalent functions, Proc. Amer. Math.
Soc., 49(1975), no. 1, 109-115.
S. S. Miller and P. T. Mocanu, "Second-order differential inequalities in
thecomplex plane,”Journal of Mathematical Analysis and Applications,
vol. 65, no. 2, 1978, 289-305.
S.S. Miller and P.T. Mocanu, "Differential subordination and univalent
functions," Mich. Math. 28(1981), 157-171.
S.S. Miller, P.T. Mocanu, Differential subordinations: theory and
applications, in: series on monographs and textbooks in Pure and Applied
Mathematics, Vol. 225, Marcel Dekker, New York and Basel, (2000).
S. Owa, On certain classes of p-valent functions with negative
coefficients, Simon Stevin, 59(1985), no. 4, 385-402.
S. Owa, “The Quasi-Hadamard Products of Certain Analytic Functions,”
In: H. M. Srivastava and S. Owa, Eds., Current Topics in Analytic Function
Theory, World Scientific Publishing Company, Singapore, 1992, 234- 251.
Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1952.
