Volume 16, Issue 1

In this paper, we introduce some iterative schemes for finding a common element of the set of fixed points of a k -strict pseudo-contractive mapping, the set of solutions of the variational inequality and the set of solutions of an equilibrium problem in a Hilbert space. The authors use the convex combination technique to show that the iterative sequences converge strongly to a common element of the three sets. The results of this paper extend and improve the results of Y. Su et al. [Nonlinear Anal: 2007], S. Plubtieng and R. Punpaeng [Appl. Math. Comput.: 2007], X. Qin et al. [Nonlinear Anal.: 2007] and S. Takahashi and W. Takahashi [J. Math. Anal. Appl. 331: 506–515, 2007].

The existence of positive solution is considered for a singular higher-order boundary value problem, where the nonlinear term is a strong Carathéodory function. Two new existence theorems are proved by applying the Lebesgue dominated convergence theorem, the Fatou lemma and the Krasnosel'skii fixed point theorem of cone expansion or cone compression type.

Aim of this work is to extend the results of Clément, Da Prato and Prüss [Rend. Istit. Mat. Univ. Trieste 29: 207–220, 1997] on the fractional white noise perturbation with Hurst parameter H ∈ (0, 1). We will obtain similar results and it will turn out that the regularity of the solution u ( t ) increases with Hurst parameter H .

In this paper, a new concept of invexity for locally Lipschitz vector-valued functions is introduced, called V - r -type I functions. The generalized Karush–Kuhn–Tucker sufficient optimality conditions are proved and duality theorems are established for a nonsmooth multiobjective optimization problems involving V - r -type I functions with respect to the same function η .

Let K be a nonempty closed convex subset of a real reflexive Banach space E with uniformly Gâteuax differentiable norm. Let T 1 , T 2 , . . . , T m : K → K be m Lipschitz mappings (for some m ∈ ℕ) such that . We construct a new iteration process and prove that the iteration process converges strongly to a common fixed point of these mappings provided at least one of the mappings is pseudocontractive. We also obtain as easy corollaries convergence results for finite families of Lipschitz pseudocontractive mappings and nonexpansive mappings. Furthermore, We prove that a slight modification of our iteration process converges strongly to a common zero of a finite family of Lipschitz accretive operators. Our new iteration process and our method of proof are of independent interest.

We denote by W + (ℂ + ) the set of all complex-valued functions defined in the closed right half plane ℂ + ≔ { s ∈ ℂ | Re( s ) ≥ 0} that differ from the Laplace transform of functions from L 1 (0, ∞) by a constant. Equipped with pointwise operations, W + (ℂ + ) forms a ring. It is known that W + (ℂ + ) is a pre-Bézout ring. The following properties are shown for W + (ℂ + ): W + (ℂ + ) is not a GCD domain, that is, there exist functions F 1 , F 2 in W + (ℂ + ) that do not possess a greatest common divisor in W + (ℂ + ). W + (ℂ + ) is not coherent, and in fact, we give an example of two principal ideals whose intersection is not finitely generated. We will also observe that W + (ℂ + ) is a Hermite ring, by showing that the maximal ideal space of W + (ℂ + ), equipped with the Gelfand topology, is contractible.

In this paper we develop a new method for valuing universal life policies via a zero-coupon bond replicating portfolio. The method combines the idea of replicating portfolio with that of a fixed point. In addition, we accompany the proposed method with an equation relating account value, reserve and present value of future profits.

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following two-point discrete boundary value problem with p -Laplacian: Δ( φ p (Δ u ( k – 1))) + e ( k )ƒ( u ( k )) = 0, k ∈ N (1, T ), u (0) – B 0 (Δ u (0)) = 0, u ( T + 1) + B 1 (Δ u ( T )) = 0. The main tool is the monotone iterative technique.

The continuous solutions of a composite functional equation are characterized. An application to the problem of invariant curves is presented.

The collection of Baire class one, Darboux functions from [0, 1] to ℝ is a rich class of functions that has been intensely investigated and characterized over the years. Which Baire class one, real-valued functions defined on [0, 1] × [0, 1] form the most “natural” extension of this class to the two-variable setting is debatable, with many suggestions having been advanced. In light of recent interest in Darboux-like properties for derivatives (i.e. gradients) of differentiable functions of two variables, it seems that now is a good time to consider some of the most feasible notions of “Darboux-like” and investigate the relationships between them.

The generalized compact-open topology τ C on partial continuous functions with closed domains in X and values in Y is studied. If Y is a non-countably compact Čech-complete space with a G δ -diagonal, then τ C is Čech-complete, sieve complete and satisfies the p -space property of Arhangel'skiǐ, respectively, if and only if X is Lindelöf and locally compact. Lindelöfness, paracompactness and normality of τ C is also investigated. New results are obtained on Čech-completeness, sieve completeness and the p -space property for the compact-open topology on the space of continuous functions with a general range Y .