q–analogue of generalized Ruschweyh operator related to a new subfamily of multivalent functions

Shahram Najafzadeh 1  and Mugur Acu 2
  • 1 Payame Noor University, Tehran
  • 2 Lucian Blaga University of Sibiu, 550012, Sibiu


A new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.

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  • [1] F. Al-Oboudi, K. Al-Amoudi, On classes of analytic functions related to conic domains, J. Math. Anal. Appl., vol. 339, no. 1, 2008, 655-667.

  • [2] F. M. Al-Oboudi, On univalent functions defined by a generalized Sălăgean operator, Int. j. math. math. sci., vol. 2004, no. 27, 2004, 1429-1436.

  • [3] G. Gasper, M. Rahman. Basic hypergeometric series, vol. 35 of Encyclopedia of Mathematics and its Applications, Cambridge university press Cambridge, UK, 1990.

  • [4] F. H. Jackson, On qfunctions and a certain difference operator, Earth Env. Sci. Trans. Roy. Soc. Edinb., vol 46, no. 2, 1909, 253-281.

  • [5] L. Jasoria, S. Bissu, On certain generalized fractional qintegral operator of pvalent functions, International Journal on Future Revolution in Computer Science Communication Engineering, vol. 3, no. 8, 2015, 230-236.

  • [6] I. B. Jung, Y. C. Kim, H. Srivastava, The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl., vol. 176, no. 1, 1993, 138-147.

  • [7] Y. Komato, On analytic prolongation of a family of operators, Mathematica (Cluj), vol. 39, no. 55, 1990, 141-145.

  • [8] S. D. Purohit, R. K. Raina, Certain subclasses of analytic functions associated with fractional qcalculus operators, Math. Scand., vol. 109, no. 1, 2011, 55-70.

  • [9] S. Ruscheweyh, New criteria for univalent functions, Proc. Am. Math. Soc., vol. 49, no. 1, 1975, 109-115.

  • [10] G. S. Salagean, Subclasses of univalent functions, Complex Analysis: Fifth Romanian-Finnish Seminar, Part I Bucharest, Lecture Notes in Mathematics 1013, Springer-Verlag, 1983.

  • [11] K. Selvakumaran, S. D. Purohit, A. Secer, M. Bayram, Convexity of certain qintegral operators of pvalent functions, Abstr. Appl. Anal., Hindawi, 2014.


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