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

Najafzadeh, Shahram; Acu, Mugur

doi:10.2478/gm-2019-0015

Abstract

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.

References

[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, 655-667.10.1016/j.jmaa.2007.05.087
Search in Google Scholar Back to article
[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.
Search in Google Scholar Back to article
[3] G. Gasper, M. Rahman. Basic hypergeometric series, vol. 35 of Encyclopedia of Mathematics and its Applications, Cambridge university press Cambridge, UK, 1990.
Search in Google Scholar Back to article
[4] F. H. Jackson, On q–functions and a certain difference operator, Earth Env. Sci. Trans. Roy. Soc. Edinb., vol 46, no. 2, 1909, 253-281.10.1017/S0080456800002751
Search in Google Scholar Back to article
[5] L. Jasoria, S. Bissu, On certain generalized fractional q–integral operator of p–valent functions, International Journal on Future Revolution in Computer Science Communication Engineering, vol. 3, no. 8, 2015, 230-236.
Search in Google Scholar Back to article
[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, 138-147.10.1006/jmaa.1993.1204
Search in Google Scholar Back to article
[7] Y. Komato, On analytic prolongation of a family of operators, Mathematica (Cluj), vol. 39, no. 55, 1990, 141-145.
Search in Google Scholar Back to article
[8] S. D. Purohit, R. K. Raina, Certain subclasses of analytic functions associated with fractional q–calculus operators, Math. Scand., vol. 109, no. 1, 2011, 55-70.10.7146/math.scand.a-15177
Search in Google Scholar Back to article
[9] S. Ruscheweyh, New criteria for univalent functions, Proc. Am. Math. Soc., vol. 49, no. 1, 1975, 109-115.10.1090/S0002-9939-1975-0367176-1
Search in Google Scholar Back to article
[10] G. S. Salagean, Subclasses of univalent functions, Complex Analysis: Fifth Romanian-Finnish Seminar, Part I Bucharest, Lecture Notes in Mathematics 1013, Springer-Verlag, 1983.10.1007/BFb0066543
Search in Google Scholar Back to article
[11] K. Selvakumaran, S. D. Purohit, A. Secer, M. Bayram, Convexity of certain q–integral operators of p–valent functions, Abstr. Appl. Anal., Hindawi, 2014.10.1155/2014/925902
Search in Google Scholar Back to article

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

Abstract

Paradigm

My account