q-STARLIKE FUNCTIONS OF ORDER ALPHA
For all q 2 0; 1 and 0 ne a class of analytic functions, so-called q-starlike functions of order on the open unit disc D = fz : jzj .
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- Goodman, A.W., (1983) Univalent functions. Vol. I, Mariner Publishing Co., Inc., Tampa, FL, 1983. MR 704183.
- Janowski, W., (1973) Some extremal problems for certain families of analytic functions, I. Ann. Polon. Math., 28, pp. 297-326.
- Kac, V. and Cheung, P., (2001) Quantum Calculus, Springer, doi: 10.1007/978-1-4613-0071-7.
- Polato˘glu, Y., ¨Ozkan, H.E., Aydo˘gan, M. and S¸en, A.Y., (2015) Distortion and growth theorems for q-Starlike functions, Rocky Mountain Journal, (submitted).
- Jackson, F.H., (1910) q-Difference equations, American Journal of Mathematics 32 (4), pp. 305-314.
- Purohit, S.D. and Raina, R.K., (2011) Certain subclass of analytic functions associated with fractional q-calculus operators, Mathematica Scandinavica, 109(1), pp. 55-70.
- Purohit, S.D., (2012) A new class of multivalently analytic functions associated with fractional q- calculus operators, Fractional Differential Calculus, 2(2), pp. 129-138.
- Purohit, S.D. and Raina, R.K., (2013) Fractional q-calculus and certain subclass of univalent analytic functions, Mathematica (Cluj), 55(78), pp. 62-74.
- Purohit, S.D. and Raina, R.K., (2014) Some classes of analytic and multivalent functions associated with q-derivative operators, Acta Universitatis Sapientiae, Mathematica, 6(1), pp. 5-23.