Certain New Subclass of Multivalent Q-Starlike Functions Associated with Q-Symmetric Calculus

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Abstract

In our present investigation, we extend the idea of q-symmetric derivative operators to multivalent functions and then define a new subclass of multivalent q-starlike functions. For this newly defined function class, we discuss some useful properties of multivalent functions, such as the Hankel determinant, symmetric Toeplitz matrices, the Fekete–Szego problem, and upper bounds of the functional ap+1−μap+12 and investigate some new lemmas for our main results. In addition, we consider the q-Bernardi integral operator along with q-symmetric calculus and discuss some applications of our main results.

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The quantum group SUq(2) and a q-analogue of the boson operators

L. C. Biedenharn (1989)

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XI.—On q-Functions and a certain Difference Operator

F. Jackson (1909)

In this paper my object is, primarily, to investigate the properties of a certain operative symbolwhich appears to be of great utility in discussingq-functions. The first part of the paper will consist of an investigation into the various forms of and the nature of the inverse operations symbolised by Δ−n . With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function ofx.