Some subordination results for certain class with complex order defined by Salagean type q-difference operator

Some subordination results for certain class with complex order defined by Salagean type q-difference operator

Автор: Aouf Mohamed K., Seoudy Tamer M.

Журнал: Владикавказский математический журнал @vmj-ru

Статья в выпуске: 4 т.22, 2020 года.

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The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Also, we derive some geometric properties such as sufficient condition and several subordination results for functions belonging to this subclass. The results presented here would provide extensions of those given in earlier works.

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Q-производный оператор, analytic function, subordinating factor sequence, hadamard product (or convolution), q-derivative operator, salagean operator

Короткий адрес: https://sciup.org/143172467

IDR: 143172467   |   DOI: 10.46698/q5183-3412-9769-d

Список литературы Some subordination results for certain class with complex order defined by Salagean type q-difference operator

  • Blboaca, T. Differential Subordinations and Superordinations, New Results, Cluj-Napoca, House of Scientific Boook Publ., 2005.
  • Miller, S. S. and Mocanu, P. T. Differential Subordinations. Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math., no. 255, New York, Marcel Dekker Inc., 2000, 480 p. DOI: 10.1201/9781482289817
  • Annaby, M. H. and Mansour, Z. S. q-Fractional Calculus and Equations, Lecture Notes in Mathematics, vol. 2056, Berlin, Springer-Verlag, 2012. DOI: 10.1007/978-3-642-30898-7
  • Aouf, M. K. and Seoudy, T. M. Convolution Properties for Classes of Bounded Analytic Functions with Complex Order Defined by q -Derivative Operator, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2019, vol. 113, no. 2, pp. 1279-1288. DOI: 10.1007/s13398-018-0545-5
  • Aral, A., Gupta, V. and Agarwal, R. P. Applications of q -Calculus in Operator Theory, New York, Springer, 2013. DOI: 10.1007/978-1-4614-6946-9
  • Gasper, G. and Rahman, M. Basic Hypergeometric Series, Cambridge, Cambridge University Press, 1990, xx+287 p.
  • Jackson, F. H. On q -Functions and a Certain Difference Operator, Transactions of the Royal Society of Edinburgh, 1908, vol. 46, pp. 253-281.
  • DOI: 10.1017/S0080456800002751
  • Seoudy, T. M. and Aouf, M. K. Convolution Properties for Certain Classes of Analytic Functions Defined by q -Derivative Operator, Abstract and Applied Analysis, vol. 2014, art. ID 846719, pp. 1-7.
  • DOI: 10.1155/2014/846719
  • Seoudy, T. M. and Aouf, M. K. Coefficient Estimates of New Classes of q -Starlike and q -Convex Functions of Complex Order, Journal of Mathematical Inequalities, 2016, vol. 10, no. 1, pp. 135-145.
  • DOI: 10.7153/jmi-10-11
  • Govindaraj, M. and Sivasubramanian, S. On a Class of Analytic Functions Related to Conic Domains Involving q -Calculus, Analysis Mathematica, 2017, vol. 43, no. 3, pp. 475-487.
  • DOI: 10.1007/s10476-017-0206-5
  • Salagean, G. S. Subclasses of Univalent Functions, Lecture Notes in Mathematics, vol. 1013, Berlin, Springer-Verlag, 1983, pp. 362-372.
  • DOI: 10.1007/BFb0066543
  • Aouf, M. K. and Srivastava, H. M. Some Families of Starlike Functions with Negative Coefficients, Journal of Mathematical Analysis and Applications, 1996, vol. 203, no. 3, pp. 762-790.
  • DOI: 10.1006/jmaa.1996.0411
  • Sivasubramanian, S., Mohammed, A. and Darus, M. Certain Subordination Properties for Subclasses of Analytic Functions Involving Complex Order, Abstract and Applied Analysis, vol. 2011, art. ID 375897, pp. 1-8.
  • DOI: 10.1155/2011/375897
  • Aouf, M. K. Subordination Properties for a Certain Class of Analytic Functions Defined by the Salagean Operator, Applied Mathematics Letters, 2009, vol. 22, no. 10, pp. 1581-1585.
  • DOI: 10.1016/j.aml.2009.05.005
  • Wilf, H. S. Subordinating Factor Sequence for Convex Maps of the Unit Circle, Proceedings of the American Mathematical Society, 1961, vol. 12, pp. 689-693.
  • DOI: 10.1090/S0002-9939-1961-0125214-5
  • Attiya, A. A. On Some Application of a Subordination Theorems, Journal of Mathematical Analysis and Applications, 2005, vol. 311, no. 2, pp. 489-494.
  • DOI: 10.1016/j.jmaa.2005.02.056
  • Srivastava, H. M. and Attiya, A. A. Some Subordination Results Associated with Certain Subclass of Analytic Functions, Journal of Inequalities in Pure and Applied Mathematics, 2004, vol. 5, no. 4, pp. 1-6.
  • Aouf, M. K. and Mostafa, A. O. Some Subordination Results for Classes of Analytic Functions Defined by the Al-Oboudi-Al-Amoudi, Archiv der Mathematik, 2009, vol. 92, pp. 279-286.
  • DOI: 10.1007/s00013-009-2984-x
  • Aouf, M. K., Shamandy, A. A., Mostafa, O. and El-Emam, F. Subordination Results Associated with β -Uniformly Convex and Starlike Functions, Proceedings of the Pakistan Academy of Sciences, 2009, vol. 46, no. 2, pp. 97-101.
  • Aouf, M. K., Shamandy, A., Mostafa, A. O. and Adwan, E. A. Subordination Results for Certain Class of Analytic Functions Defined by Convolution, Rendiconti del Circolo Matematico di Palermo, 2011, vol. 60, pp. 255-262.
  • DOI: 10.1007/s12215-011-0048-0
  • Aouf, M. K. Shamandy, A. Mostafa, A. O. and Adwan, E. A. Subordination Theorem for Analytic Functions Defined by Convolution, Complex Analysis and Operator Theory, 2013, vol. 7, pp. 1117-1126.
  • DOI: 10.1007/s11785-011-0171-0
  • Bulut, S. and Aouf, M. K. Subordination Properties for a Certain Class of Analytic Functions with Complex Order, Le Matematiche, 2014, vol. 69, no. 2, pp. 117-128.
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