Φ, sup
ثبت نشده
چکیده
Well-posedness of constrained minimization problems via saddle-points BIAGIO RICCERI Dedicated to Professor Jean Saint Raymond on his sixtieth birthday, with my greatest admiration and esteem Here and in the sequel, X is a Hausdorff topological space, J, Φ are two real-valued functions defined in X, and a, b are two numbers in [−∞, +∞], with a < b.
منابع مشابه
Composition Operators from the Hardy Space to the Zygmund-Type Space on the Upper Half-Plane
and Applied Analysis 3 In two main theorems in 20 , the authors proved the following results, which we now incorporate in the next theorem. Theorem A. Assume p ≥ 1 and φ is a holomorphic self-map of Π . Then the following statements true hold. a The operator Cφ : H Π → A∞ Π is bounded if and only if sup z∈Π Im z ( Imφ z )1/p < ∞. 1.8 b The operator Cφ : H Π → B∞ Π is bounded if and only if sup ...
متن کاملSe p 20 04 ON THE MIXING COEFFICIENTS OF PIECEWISE MONOTONIC MAPS
We investigate the mixing coefficients of interval maps satisfying Rychlik’s conditions. A mixing Lasota-Yorke map is reverse φ-mixing. If its invariant density is uniformly bounded away from 0, it is φ-mixing iff all images of all orders are big in which case it is ψ-mixing. Among β-transformations, non-φ-mixing is generic. In this sense, the asymmetry of φ-mixing is natural. §0 Introduction M...
متن کامل2 00 9 On an elliptic Kirchhoff - type problem depending on two parameters BIAGIO RICCERI
Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...
متن کاملOn an elliptic Kirchhoff-type problem depending on two parameters
Let Ω ⊂ R be a bounded domain with smooth boundary, and let K : [0,+∞[→ R be a given continuous function. If n ≥ 2, we denote by A the class of all Carathéodory functions φ : Ω×R → R such that sup (x,t)∈Ω×R |φ(x, t)| 1 + |t|q < +∞ , where 0 < q < n+2 n−2 if n > 2 and 0 < q < +∞ if n = 2. While, when n = 1, we denote by A the class of all Carathéodory functions φ : Ω ×R → R such that, for each r...
متن کاملUnique Positive Almost Periodic Solution for Discrete Nonlinear Delay Survival Red Blood Cells Model
and Applied Analysis 3 the hull of f . It is easy to see that if f n is almost periodic, then for all f1 ∈ H f , lim inf n→∞ f n inf n∈Z f n inf n∈Z f1 n , lim sup n→∞ f n sup n∈Z f n sup n∈Z f1 n . 1.7 Definition 1.2. Let f : Z × C → R. Then f is said to be almost periodic in n ∈ Z uniformly on compact set of C, if f n, · is continuous for each n ∈ Z, and for any > 0 and every compact setK ⊂ C...
متن کاملStrong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces
and Applied Analysis 3 where ∂ denotes the subdifferential in the sense of convex analysis. We need the subdifferential inequality Φ( x + y ) ≤ Φ (‖x‖) + ⟨y, j (x + y)⟩ ∀x, y ∈ X, j (x + y) ∈ Jφ (x + y) . (14) For a smoothX, we have Φ( x + y ) ≤ Φ (‖x‖) + ⟨y, Jφ (x + y)⟩ ∀x, y ∈ X, (15) or considering the normalized duality mapping J, we have x + y 2 ≤ ‖x‖ 2 + 2 ⟨y, J (...
متن کامل