Abstract. Using of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benitez, K. PrzesÃlawski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are character...

The objective of this paper is to introduce a general scheme for deriving a posteriori error estimates by using duality theory of the calculus of variations. We consider variational problems of the form inf v∈V {F (v) +G(Λv)}, where F : V → R is a convex lower semicontinuous functional, G : Y → R is a uniformly convex functional, V and Y are reflexive Banach spaces, and Λ : V → Y is a bounded l...

The goal of the present paper is to investigate some characterization for generalized Struve functions of first kind to be in the new subclasses of β uniformly starlike and β uniformly convex functions of order α. Further we point out some consequences of our main results. Mathematics subject classification: 30C45.

In this paper, we consider some sufficient conditions for two integral operators to be starlike, close-to-convex and uniformly convex functions defined in the open unit disk. Mathematics subject classification (2000): 30C45.

The function Df , called the Bregman distance associated with f , is always well defined because ∂f(x) is nonempty and bounded, for all x ∈ X (see, e.g., [22]), so that the infimum in (1.1) cannot be −∞. It is easy to check that Df (x, y) ≥ 0 and that Df (x, x) = 0, for all x, y ∈ X. If f is strictly convex then Df (x, y) = 0 only when x = y. For t ∈ [0,∞) and z ∈ X let U(z, t) = {x ∈ X : ‖x− z...

The aim of this paper is to present some existence results for nearest-point and farthestpoint problems, in connection with some geometric properties of Banach spaces. The idea goes back to Efimov and Stečkin who, in a series of papers (see [28, 29, 30, 31]), realized for the first time that some geometric properties of Banach spaces, such as strict convexity, uniform convexity, reflexivity, an...

for some α (0 α< 1). We denote by p(α) the subclass of p consisting of functions which are p-valently convex of order α in U. In particular, we denote 1(0)= . A function f(z)∈ 1 is said to be uniformly convex inU if f(z) is in the class and has the property that the image arc f(γ) is convex for every circular arc γ contained in U with center at t ∈ U. We also denote by the subclass of 1 consist...