Some new applications of Integral and Differential operator for new subclasses of analytic functions
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Keywords:Analytic functions, q-Calculus, Integral operators, Convolution, Starlike and Convex functions, Differential subordination..
In this paper, we consider convolution operatorz D_x h(z)=h(z)*z/(1-xz)(1-z) , and define a new differential operator D_(λ,x)^m on the analytic functions in the complex plane, for all x,|x|≤1. For x=1 the operator becomes the Al Oboudi differential operator and for real number x=q and λ=1, 0 < q < 1, we obtain the Salagean q-differential operator. Furthermore, we consider this operator D_(λ,x)^m and then define two new integral operators. We discuss some interesting applications of these operators by introducing several new subclasses of analytic functions. Also geometric properties are investigated for integral operators on new subclasses of analytic functions and some subordination results are discussed for differential operatorD_(λ,x)^m . .
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