In this paper, we consider a subclass S Σ (α, β ) of bi-univalent functions defined in the open unit disk D = {z ∈ C : |z| < 1}. Besides, we find upper bounds for the second and third coefficients for functions in this subclass.
This paper investigates the nonlinear boundary value problem, resulting from the exact reduction of the Navier–Stokes equations for unsteady laminar boundary layer flow caused by a stretching surface in a quiescent viscous incompressible fluid. We prove existence of solutions for all values of the relevant parameters and provide unique results in the case of a monotonic solution. The results are obtained using a topological shooting argument, which varies a parameter related to the axial shear stress. To solve this equation, a numerical method is proposed based on a rational Chebyshev functions spectral method. Using the operational matrices of derivative, we reduced the problem to a set of algebraic equations. We also compare this work with some other numerical results and present a solution that proves to be highly accurate. Copyright © 2016 John Wiley & Sons, Ltd.
The primary motivation of the paper is to define a new class C h δ α , β , γ which consists of univalent functions associated with Chebyshev polynomials. For this class, we determine the coefficient bound and convolution preserving property. Furthermore, by using subordination structure, two new subclasses of C h δ α , β , γ are introduced and denoted by M λ 1 , λ 2 , s and N λ 1 , λ 2 , s , respectively. For these subclasses, we obtain coefficient estimate, extreme points, integral representation, convexity, geometric interpretation, and inclusion results. Moreover, we prove that, under some restrictions on parameters, C h δ α , β , γ = N λ 1 , λ 2 , s .
In this paper, we study reproducing kernels whose ranges are subsets of a C *algebra or a Hilbert C * -module. In particular, we show how such a reproducing kernel can naturally be expressed in terms of operators on a Hilbert C * -module. We focus on relative reproducing kernels and extend this concept to such spaces associated with cocycles.
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