The results obtained by the authors in present paper refer to quantum calculus applications regarding theories of differential subordination and superordination. These are established means an operator defined as q-analogue multiplier transformation. Interesting superordination derived involving functions belonging a new class normalized analytic open unit disc U, which is investigated here usi...

For functions p analytic in the open unit disc U = {z : |z|< 1} with the normalization p(0)= 1, we consider the families [A,−1], −1 0, consisting of p, which have the disc formulation |p−1|< b in U . We then introduce subordination criteria for the choice of p(z)= zf ′(z)/f(z), where f is analytic in U and n...

Recently, the properties of analytic functions have been mainly discussed by means a fuzzy subset and q-difference operator. We define certain new subclasses using subordination to univalent whose range is symmetric with respect real axis. introduce family linear q-operators various classes associated these operators. The inclusion results integral are main investigations this article.

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...

In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in open unit disk, with respect to subordination. We give an elementary proof establish some estimates coefficient bounds new class. conclude study by giving result Fekete-Szegö theorem. A corollary was given show results subclasses our

Subclasses of analytic and bi-univalent functions have been extensively improved utilized for estimating the Taylor–Maclaurin coefficients Fekete–Szegö functional. In this paper, we consider a certain subclass normalized functions. These inverses that possess continuation to an open unit disk are associated with orthogonal polynomials; namely, Gegenbauer polynomials satisfy subordination condit...