Volume 14, Issue 2

Let A and B be sets of real sequences. Let F ( A, B ) denote the set of all functions ƒ : ℝ → ℝ that preserve A and B in the sense that (ƒ( a n )) ∈ B for all sequences ( a n ) ∈ A . We characterize F ( A, B ) when A and B are convergent series, absolutely convergent series, relatively convergent series and divergent series.

In this article we prove local interior and boundary Lipschitz continuity of the solutions of a general class of elliptic free boundary problems in divergence form.

Using the Wright's generalized hypergeometric function, we investigate a class W ( q, s; A, B , λ) of analytic functions with negative coefficients. We derive many results for the modified Hadamard product of functions belonging to the class W ( q, s; A, B , λ). Moreover, we generalize some of the distortion theorems to the classical fractional integrals and derivatives and the Saigo (hypergeometric) operators of fractional calculus.

In the present paper, some generalized critical points theorems for locally Lipschitz functions are given, and some classical important theorems are improved.

We study the stability of the zero solution of an impulsive set differential system with delay by means of the perturbing Lyapunov function method. Sufficient conditions for the stability of the zero solution of impulsive set differential equations with delay are presented.

In this paper, an existence result of quasi-equilibrium problem is proved and used to establish the existence of weighted Nash equilibria for constrained multi-criteria games under a generalized quasi-convexity condition and a coercivity type condition on the payoff functions. As consequence, we prove the existence of Pareto equilibria for constrained multi-criteria games with non-compact strategy sets in topological vector spaces.

For each pointclass Γ ⊆ P (2 ω ) define U [Γ] as the collection of all X ⊆ 2 ω such that the preimage ƒ –1 ( X ) belongs to Γ for each continuous ƒ : 2 ω → 2 ω . We study the properties of and possible relationships among the classes U [Γ], where Γ ranges over the σ -algebras ( l ), ( m ), the completely Ramsey sets, and the sets with the Baire property. We also prove some results about cardinal coefficients of U [Γ] for the general case of Marczewski-Burstin representable σ -algebras Γ. We finish by posing some unsolved problems.

In this paper, we study the stabilization problem of uncertain systems. We treat a class of uncertain systems whose nominal part is affine in the control and whose uncertain part is bounded by a known affine function of the control, when the control is bounded by a specified constant.

Let (Ω, A , P ) be a complete probability space. We show that the trivial function is the unique L 1 -solution of the following refinement type equation for a wide class of the given functions φ . This class contains functions of the form φ ( x, ω ) = α ( ω ) x – β ( ω ) with –∞ < ∫ Ω log| α ( ω )| dP ( ω ) < 0.

In this paper, we study fixed points of solutions of the differential equation ƒ″ + A 1 ( z ) ƒ′ + A 0 ( z ) ƒ = 0, where A j ( z ) (≢ 0) ( j = 0, 1) are transcendental meromorphic functions with finite order. Instead of looking at the zeros of ƒ ( z ) – z , we proceed to a slight generalization by considering zeros of g ( z ) – φ ( z ), where g is a differential polynomial in ƒ with polynomial coefficients, φ is a small meromorphic function relative to ƒ, while the solution ƒ is of infinite order.

Motivated by Gupta [A non-resonant multi-point boundary value problem for a p-Laplacian type operator: 143–152, 2003] and Garcia-Huidobro, Gupta, Manasevich [Nonlinear Anal. 56: 1071–1089, 2004], the solvability of multi-point boundary value problems consisting of higher-order differential equations and multi-point boundary conditions are studied in this paper, respectively. Results show us that known theorems are complemented and improved. Numerical examples are presented to demonstrate the main theorems.