On a subclass of p-valent analytic functions involving fractional q-calculus operators
Keywords:
Analytic functions, p-valent functions, fractional q-calculus operators, coefficient bounds, distortion theorems.Abstract
In this paper, we consider a new subclass of p-valent analytic functions in the open unitdisk involving a fractional q-differeintegral operator. For this subclass of functions,we derive the coefficient inequality and some distortion theorems. Special cases of themain results are also mentioned.
References
Gasper, G. & Rahman, M. 1990. Basic Hypergeometric Series, Cambridge
University Press, Cambridge.
Ismail, M. E. H. & Muldoon, M. E. 1994. Inequalities and monotonicity properties
for gamma and q-gamma functions, pp. 309-323 in R.V.M. Zahar, ed.,
Approximation and Computation: A Festschrift in Honor of Walter Gautschi,
ISNM, vol. 119, Birkhauser, Boston-Basel-Berlin.
Owa, S. & Srivastava, H.M. 1985. Certain classes of multivalent functions with
negative coefficients, Bulletin of the Korean Mathematical Society, 22: 101-116.
Purohit, S.D. 2012. A new class of multivalently analytic functions associated with
fractional q-calculus operators, Fractional Differential Calculus, 2(2): 129-138.
Purohit, S.D. & Raina, R.K. 2011. Certain subclass of analytic functions associated
with fractional q-calculus operators, Mathematica Scandinavica, 109(1): 55-70.
S.D. Purohit and R.K. Raina
Purohit, S.D. & Raina, R.K. 2013. Fractional q-calculus and certain subclass of
univalent analytic functions, Mathematica (Cluj), 55(78)(1), 62-74.
Purohit, S.D. & Raina, R.K. 2014. Some classes of analytic and multivalent
functions associated with q-derivative operators, Acta Universitatis Sapientiae,
Mathematica, 6(1), 5-23.
Raina, R.K. & Nahar, T.S. 2002. On certain subclasses of p-valent functions defined
in terms of certain fractional derivative operators, Glasnik Matematicki, 37(1):
-71.
Shukla, S.L. & Dashrath 1984. On certain classes of multivalent functions with
negative coefficients, Pure & Applied Mathematika Sciences, 20: 63-72.