In this investigation, the q-difference operator and S?l?gean q-differential are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine general Taylor–Maclaurin coefficient functions in class using Faber polynomial method. demonstrate unpredictable behaviour initial coefficients a2, a3 investigate Fekete–Szeg? problem a3?a22 for To highlight connections ...

We propose and justify an explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation for bounded linear operators on Banach space.

The zero-truncated Poisson distribution is an important and appropriate model for many real-world applications. Here, we exploit the probabilities to construct a new subclass of analytic bi-univalent functions involving Gegenbauer polynomials. For in constructed class, explore estimates Taylor–Maclaurin coefficients a2 a3, next, solve Fekete–Szegő functional problem. A number interesting result...

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

In this paper, we first modify one of the most famous theorems on principle differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using modified form, generalize and improve several results, which appeared recently in literature geometric function theory complex analysis. We also prove some simple conditions starlikeness,...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.

The object of this article is to explore a ?-pseudo-?-convex ?-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor–Maclaurin coefficient estimates functions in defined family. classical Fekete–Szegö inequalities for also estimated. Furthermore, we present some special cases main result...

This paper makes the first systematic attempt to determine using perturbation theory the positions of images by gravitational lensing due to arbitrary number of coplanar masses without any symmetry on a plane, as a function of lens and source parameters. We present a method of Taylor-series expansion to solve the lens equation under a small mass-ratio approximation. First, we investigate pertur...

The solutions provided in this work address the classic but still relevant topic of establishing new classes univalent functions linked to $q$-Chebyshev polynomials and examining coefficient estimates features. Aspects quantum calculus are also considered research make it more unique produce pleasing outcomes. We introduce connected polynomials, which generalize certain previously investigated ...