Geometric process solving a class of analytic functions using q-convolution differential operator

Abstract

In current realization, our object is to use the convolution product in terms of the notion quantum calculus to deliver a propagated q-derivative factor taking a more generalized Sàlàgean formula. By joining both the new factor together with the Janowski formula, we designate a special category of analytic factors in domain of unit disk. Finally, we deliberate a set of significant inequalities involving these classes. As applications, we seek the q-differential translator to generalize a denomination of differential equations species Briot-Bouquet and formulate its upper analytic solution using the subordination idea. This application can be employed in information theory and thermo dynamical systems.

A New Measure of Quantum Starlike Functions Connected with Julia Functions

“…Recently, Zainab et al [16] presented a sufficient condition for q-starlikeness using a special curve. In addition, different differential and integral operators are generalized utilizing QC [17][18][19][20].…”

On convolutions of slanted half-plane mappings

“…On the other hand, harmonic mappings and related functions have been used in the areas of description of the fluid flows, elasticity problems and approximation theory of plates, etc. Techniques in recent papers such as [4][5][6] can be used in further applications.…”

“…(z) = (z + C) (z + D) and * (z) = z 2 (1/z) = 1 + Cz 1 + Dz .As |(e iμ + ρ e 2iβ )/(e −iμ + ρ e −2iβ )| = 1, the result follows. Let (z) be defined by(5) so that (z) = (z + C)(z + D). Also, let ρ = |ρ| e iλ where λ = arg ρ and |ρ| < 1.…”

“…is given by(5) and * (z) = 1 + 4ρ e −iμ + e −2iβ + 3 |ρ| 2 e −2iβ 2 e −iμ + ρ e −2iβ z + 2ρ 2 e −iμ + 2ρ e −2iβ + e −iβ 1 − |ρ| 2 2 e −iμ + ρ e −2iβ z 2 .…”

A new parametric differential operator generalized a class of d'Alembert's equations

“…Nowadays, the fractional, fractal and conformable operators play a major role developing applications in engineering, medical studies including the dynamic of recent pandemic, economic and computer sciences. More applications of this theory is appeared, when some classes of differential and integral operators are extended to the complex plane [7][8][9].…”