Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

MSC2010: 30C45, 33C45

Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions

In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.

Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45

New Coefficient Conditions for Functions Starlike with Respect to Symmetric Points

2000 Mathematics Subject Classification: Primary 30C45, secondary 30C80.

On the uniform approximation of Cauchy continuous functions

In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Coefficient Estimates for Analytic Functions Concerned with Hankel Determinant

MSC 2010: 30C45

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

Some Distortion Theorems for Starlike Harmonic Functions

MSC 2010: 30C55, 30C45

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 0uniformly in k∈W, for 0⩽a⩽b. As a particular application we consider the case when the kernel takes the form k(s,t)=κ(s−t)z(t), with , , and κ(s)=O(|s|−b) as |s|→∞, for some b>1. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.