In this research contribution, we have constructed a subclass of analytic bi-univalent functions using Horadam polynomials. Bounds for certain coefficients and Fekete- Szegö inequalities been estimated.

We develop unified information-theoretic machinery for deriving lower bounds for passive and active learning schemes. Our bounds involve the so-called Alexander’s capacity function. The supremum of this function has been recently rediscovered by Hanneke in the context of active learning under the name of “disagreement coefficient.” For passive learning, our lower bounds match the upper bounds o...

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g = f−1 satisfying the conditions that zf ′(z)/f(z) and zg′(z)/g(z) are both subordinate to a starlike univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier kn...

In this paper we discuss new domain decomposition preconditioners for piecewise linear finite element discretisations of boundary-value problems for the model elliptic problem −∇ · (A∇u) = f , (1) in a bounded polygonal or polyhedral domain Ω ⊂ R, d = 2 or 3 with suitable boundary data on the boundary ∂Ω. The tensor A(x) is assumed isotropic and symmetric positive definite, but may vary with ma...

We give effectivized Hölder-logarithmic energy and regularity dependent stability estimates for the Gel’fand inverse boundary value problem in dimension d = 3. This effectivization includes explicit dependance of the estimates on coefficient norms and related parameters. Our new estimates are given in L and L∞ norms for the coefficient difference and related stability efficiently increases with...