Let E be a real Banach space with norm ∥.∥ and let J be the normalized duality mapping from E into 2E ∗ given by Jx = {x∗ ∈ E∗ : ⟨x, x∗⟩ = ∥x∥∥x∗∥, ∥x∥ = ∥x∗∥} for all x ∈ E, where E∗ denotes the dual space of E and ⟨., .⟩ denotes the generalized duality pairing between E and E∗. A Banach space E is said to be strictly convex if ∥ 2 ∥ < 1 for all x, y ∈ E with ∥x∥ = ∥y∥ = 1 and x ̸= y. It is sai...

Let X be a real strictly convex and Kadec Banach space and G a nonempty closed relatively boundedly weakly compact subset of X : Let BðX Þ (resp. KðXÞ) be the family of nonempty bounded closed (resp. compact) subsets of X endowed with the Hausdorff distance and let BGðXÞ denote the closure of the set fAABðX Þ : A-G 1⁄4 |g and KGðX Þ 1⁄4 BGðX Þ-KðXÞ: We introduce the admissible family A of BðX Þ...

and Applied Analysis 3 It is shown in [19] that if E = H, a real Hilbert space, then ρ(t) = t, for t > 0. In our general setting, throughout this paper we assume that ρ(t) ≤ 2t. Lemma 3. Let E be a real Banach space. Then the following inequality holds: 󵄩󵄩󵄩󵄩x + y 󵄩󵄩󵄩󵄩 2 ≤ ‖x‖ 2 + ⟨y, j (x + y)⟩ , ∀x, y ∈ H, j (x + y) ∈ J (x + y) . (10) Lemma 4 (see [20]). Let E be a uniformly convex Banach spac...

We show that if Lr(X), 1 < r < ∞, has an asymptotically uniformly convex renorming of power type then X admits a uniformly convex norm of power type.

Let F(a,b;c;z) be the classical hypergeometric function and f be a normalized analytic functions defined on the unit disk . Let an operator Ia,b;c(f ) be defined by [Ia,b;c(f )](z)= zF(a,b;c;z)∗f(z). In this paper the authors identify two subfamilies of analytic functions 1 and 2 and obtain conditions on the parameters a,b,c such that f ∈ 1 implies Ia,b;c(f )∈ 2.

* Correspondence: manuel. [email protected] Instituto de Investigacion y Desarrollo de Procesos, Universidad del Pais Vasco, Campus of Leioa (Bizkaia), Aptdo. 644-Bilbao, 48080Bilbao, Spain Full list of author information is available at the end of the article Abstract This article discusses a more general contractive condition for a class of extended (p ≥ 2) -cyclic self-mappings on the union of ...

We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by Σ, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is BΣ-convex if and only if it has Σ-subtype. The class of uniformly non-L(Σ) operator spaces, which is also the class of BΣ-conve...