Stability results for a much wider class of (ψ,φ)-weakly contractive mappings are proved in a metric space. These results include a number of known results. Mathematics Subject Classification: 54H25; 47H10

and Applied Analysis 3 Let β > 0. The weighted-type space or growth space on the upper half-planeA∞ β Π consists of all f ∈ H Π such that ∥ ∥f ∥ ∥ A∞ β Π sup z∈Π Iz β ∣ ∣f z ∣ ∣ < ∞. 1.7 It is easy to check thatA∞ β Π is a Banach space with the norm defined above. For weightedtype spaces on the unit disk, polydisk, or the unit ball see, for example, papers 10, 32, 33 and the references therein....

Given a classical theory T, a Kripke structure K = (K,≤, (Aα)α∈K ) is called T-normal (or locally T) if for each α ∈ K, Aα is a classical model of T. It has been known for some time now, thanks to van Dalen, Mulder, Krabbe, and Visser, that Kripke models of HA over finite frames (K,≤) are locally PA. They also proved that models of HA over the frame (ω,≤) contain infinitely many Peano nodes. We...

We consider the critical focusing NLS in 1-d of the form (1.1) i∂ t ψ + ∂ 2 x ψ = −|ψ| 4 ψ, i = √ −1, ψ = ψ(t, x), and ψ complex valued. It is well-known that this equation permits standing wave solutions of the form φ(t, x) = e iαt φ 0 (x, α), α > 0 Indeed, requiring positivity and evenness in x for φ 0 (x, α) implies for example φ 0 (x, α) = α 1 2 (3 2) 1 4 cosh 1 2 (α 2 x) Another remarkable...

In this paper, a generalization of Nadler’s fixed point theorem is presented for H-type k-multivalued weak contractive mappings. We consider a nonconvex Hammerstein type integral inclusion and prove an existence theorem by using an H-type multi-valued weak contractive mapping.

In 2006, I. Beg and M. Abbas have studied the existence of coincidence and common fixed points for two mappings satisfying a weak contractive condition. Their results were extended in 2008 by A. Azam and M. Shakeel to the case of three mappings. Recently M. Abbas and D. Dorić employed the contractive conditions introduced in [Q. Zhang and Y. Song, Fixed point theory for generalized φ-weak contr...

Lemma 2.1. Let F be a field, let E = F (α) be a simple extension of F , where α is algebraic over F and f = irr(α, F, x), let ψ : F → K be a homomorphism from F to a field K, and let L be an extension of K. If β ∈ L is a root of ψ(f), then there is a unique extension of ψ to a homomorphism φ : E → L such that φ(α) = β. Hence there is a bijection from the set of homomorphisms φ : E → L such that...