Abstract
The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.
Highlights
The exceptional importance and necessity of introducing new subclasses of analytic functions and investigating their properties, such as convexity, close-to-convexity, distortion properties, and coefficient estimates, are due to their applications in a wide variety of areas, including mathematics, physics, mechanics, electrotechnics, and many others
Ismail et al [4] were the first to use the q-derivative operator Dq to investigate a certain q-analogue of the class of starlike functions in open unit disk
We present a new class of analytic functions, defined in the open unit disk by means of a new q-difference operator, and we obtain some interesting results in this generalized class
Summary
The exceptional importance and necessity of introducing new subclasses of analytic functions and investigating their properties, such as convexity, close-to-convexity, distortion properties, and coefficient estimates, are due to their applications in a wide variety of areas, including mathematics, physics, mechanics, electrotechnics, and many others. Ismail et al [4] were the first to use the q-derivative operator Dq to investigate a certain q-analogue of the class of starlike functions in open unit disk. Srivastava et al [9] established several general results, concerning the partial sums of meromorphically starlike functions, defined by means of a certain class of q-derivative operators.
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