Convolution properties for a family of analytic functions involving q -analogue of Ruscheweyh differential operator
Convolution properties for a family of analytic functions involving q -analogue of Ruscheweyh differential operator
The main object of the present paper is to investigate convolution properties for a new subfamily of analyticfunctions that are defined by q -analogue of Ruscheweyh differential operator. Several consequences of the main resultsare also given.
___
- [1] Agrawal S, Sahoo SK. A generalization of starlike functions of order . Hokkaido Mathematical Journal 2017;
46(1): 15-27.
- [2] Ahmad B, Arif M. New subfamily of meromorphic convex functions in circular domain involving q -operator.
International Journal of Nonlinear Analysis and Applications 2018; 16(1): 75-82.
- [3] Ahuja OP. Families of analytic functions related to Ruscheweyh derivatives and subordinate to convex functions.
Yokohama Mathematical Journal 1993; 41(1): 39-50.
- [4] Aldweby H, Darus M. A subclass of harmonic univalent functions associated with q -analogue of Dziok-Srivastava
operator. ISRN Mathematical Analysis 2013; (Article 382312): 1-6.
- [5] Aldawish I, Darus M. Starlikeness of q -differential operator involving quantum calculus. Korean Journal of Mathematics
2014; 22 (4): 699-709.
- [6] Aral A, Gupta V. On q -Baskakov type operators. Demonstratio Mathematica 2009; 42(1): 109-122.
- [7] Arif M, Ahmad B. New subfamily of meromorphic starlike functions in circular domain involving q-differential
operator. Mathematica Slovaca 2018; 68(5): 1049-1056.
- [8] Arif A, Haq M, Liu JL. A subfamily of univalent functions associated with q -analogue of Noor integral operator.
Journal of Function Spaces 2018; Article ID 3818915.
- [9] Arif M, Srivastava HM, Umar S. Some applications of a q -analogue of the Ruscheweyh type operator for multivalent
functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A Matemáticas 2018; 2018:
1-11.
- [10] Barbosu D, Acu AM, Muraru CV. On certain GBS-Durrmeyer operators based on q -integers. Turkish Journal of
Mathematics 2017; 41(2): 368-380.
- [11] Ismail MEH, Merkes E, Styer D. A generalization of starlike functions. Complex Variables, Theory and Applications
1990;14: 77-84.
- [12] Jackson FH. On q -definite integrals. The Quarterly Journal of Pure and Applied Mathematics 1910; 41: 193-203.
- [13] Jackson FH. On q -functions and a certain difference operator. Earth and Environmental Science Transactions of
The Royal Society of Edinburgh 1909; 46(2): 253-281.
- [14] Janowski W. Some extremal problems for certain families of analytic functions. Annales Polonici Mathematici 1973;
28: 297-326.
- [15] Kanas S, Răducanu D. Some class of analytic functions related to conic domains. Mathematica Slovaca 2014; 64(5):
1183-1196.
- [16] Mahmmod S, Sokół J. New subclass of analytic functions in conical domain associated with Ruscheweyh q -
differential operator. Results in Mathematics 2017; 71(4): 1345-1357.
- [17] Mohammed A, Darus M. A generalized operator involving the q -hypergeometric function. Matematički Vesnik 2013;
65(4): 454-465.
- [18] Noor KI, Arif M. On some applications of Ruscheweyh derivative. Computers & Mathematics with Applications
2011; 62(12): 4726-4732.
- [19] Ruscheweyh S. New criteria for univalent functions. Proceedings of the American Mathematical Society 1975; 49:
109-115.
- [20] Seoudy TM, Aouf MK. Coefficient estimates of new classes of q -starlike and q -convex functions of complex order.
Journal of Mathematical Inequalities 2016; 10(1): 135-145.
- [21] Seoudy TM, Aouf MK. Convolution properties for certain classes of analytic functions defined by q -derivative
operator. Abstract and Applied Analysis 2014; (Article 846719): 1-7.
- [22] Silverman H, Silvia EM, Telage D. Convolution conditions for convexity starlikeness and spiral-likness. Mathematiche
Zeitschrift 1978; 162(2): 125-130.
- [23] Silverman H. Univalent functions with negative coefficients. Proceeding of the American Mathematical Society 1975;
51: 109-116.
- [24] Srivastava HM, Bansal D. Close-to-convexity of a certain family of q -Mittag-Leffler functions. Journal of Nonlinear
and Variational Analysis 2017; 1(1): 61-69.
- [25] Srivastava HM. Univalent functions, fractional calculus, and associated generalized hypergeometric functions. In:
Srivastava HM, Owa S, editors. Univalent Functions, Fractional Calculus, and Their Applications. New York, NY,
USA: Halsted Press, pp. 329-354.