Abstract
Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third Bessel functions, we derive necessary and sufficient conditions for which the new generalized operators belong to the class of q-starlike functions of order alpha. Several corollaries and consequences of the main results are also pointed out.
Highlights
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The concept of q-starlike functions was introduced by Ismail et al [3] in 1990
In [14], Agrawal and Sahoo introduced the class of q-starlike functions of order α, denoted by Sq∗ (α)
Summary
The concept of q-starlike functions was introduced by Ismail et al [3] in 1990. The mathematical description and implementations of the fractional q-derivative operators and fractional q-calculus in geometric function theory were methodically explored [4]. Studied some classes of q-starlike functions related with conic region.
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