In the present paper, sharp upper bounds of |a3 − μa2| for the functions f(z) = z+ a2z + a3z + ... belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractiona...

In the present paper, sharp upper bounds of |a3 −μa2| for the functions f(z) = z + a2z + a3z + · · · belonging to a new subclass of Sakaguchi type functions are obtained. Also, application of our results for subclass of functions defined by convolution with a normalized analytic function are given. In particular, Fekete-Szegö inequalities for certain classes of functions defined through fractio...

The objective of this work is to provide a methodology for approximating globally optimal Fekete point con-gurations. This problem is of obvious interest in numerical mathematics and scientic modeling. Following a brief discussion of the pertinent analytical background, Lipschitz global optimization (LGO) is applied to determine {i.e., to numerically approximate{ Fekete point congurations. Next...

In geometric function theory, Lucas polynomials and other special have recently gained importance. this study, we develop a new family of bi-univalent functions. Also examined coefficient inequalities Fekete-Szegö problem for via these polynomials.

An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and non-perturbative crossing symmetric representation of 2-2 scattering amplitudes identical scalars is pointed out. Using dispersion relation unitarity, we are able derive several inequalities, analogous those which arise discussions conjecture. We ne...

In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö type theory of orthogonal polynomials in the unit circle for several noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several noncommuting...

We consider the time–continuous doubly–dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel operator is represented by a symbol which is periodic in time and fulfills some further integrability, smoothness and oscillation conditions. More precisely, we apply the well–known HolsingerGallager model for translating a time–continuous channe...

In this paper, we define certain families SE*(?) and CE(?) of holomorphic bi-univalent functions which are defined in the open unit disk U. We establish upper bounds for initial Taylor–Maclaurin coefficients Fekete–Szegö type inequalities these families.