In the current work, we introduce a special family of function analytic and m-fold symmetric bi-univalent functions obtain estimates Taylor–Maclaurin coefficients |dm+1| |d2m+1| for in family. For ? real number, Fekete–Szegö functional |d2m+1??dm+12| is also estimated. We indicate several cases defined connections to existing results are discussed.

In this paper, we introduce and investigate new subclasses (Yamakawa-type bi-starlike functions another class of Lashin, both mentioned in the reference list) bi-univalent defined open unit disk, which are associated with Gegenbauer polynomials satisfy subordination conditions. Furthermore, find estimates for Taylor–Maclaurin coefficients |a2| |a3| these subclasses. Several known or consequence...

Motivated by q-calculus, we define a new family of Σ, which is the bi-univalent analytic functions in open unit disc U that related to Einstein function E(z). We establish estimates for first two Taylor–Maclaurin coefficients |a2|, |a3|, and Fekete–Szegö inequality a3−μa22 belong these families.

The purpose of this article is to introduce a new subclass analytic and bi-univalent functions, in associated with sigmoid function investigate the upper bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Further we obtain Fekete-Szego inequalities class sigma. We also give several illustrative examples functionclass which here.

Coinduction is often seen as a way of implementing innnite objects 8, 44. Since real numbers are typical innnite objects, it may not come as a surprise that calculus, when presented in a suitable way, is permeated by coinductive reasoning. What is surprising is that mathematical techniques, recently developed in the context of computer science, seem to be shedding a new light on some basic meth...

Abstract. Some prediction properties of the t-transformation of Levin are analyzed for two kinds of limiting processes. It is shown under certain circumstances that when the t-transformation is applied to a power series, the coefficients of the Maclaurin series of the rational approximation obtained approximate those of the given series with increasing accuracy. Theoretical and numerical exampl...

this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...