The dual of the James Tree space is asymptotically uniformly convex.

We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.

We give several sufficient conditions on a pair of Banach spaces X and Y under which each Lipschitz mapping from a domain in X to Y has, for every ǫ > 0, a point of ǫ-Fréchet differentiability. Most of these conditions are stated in terms of the moduli of asymptotic smoothness and convexity, notions which appeared in the literature under a variety of names. We prove, for example, that for ∞ > r...

In this paper, we study the properties of the metric projection operator (the nearest point projection operator) and its continuity. Then we use it to solve variational inequalities in general Banach spaces and to approximate the solutions in uniformly convex and uniformly smooth Banach spaces.

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...

Let K be a compact convex body in R, let Kn be the convex hull of n points chosen uniformly and independently in K, and let fipKnq denote the number of i-dimensional faces of Kn. We show that for planar convex sets, Erf0pKnqs is increasing in n. In dimension d ě 3 we prove that if limnÑ8 Erfd ́1pKnqs Anc “ 1 for some constants A and c ą 0 then the function n ÞÑ Erfd ́1pKnqs is increasing for n la...

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem, the set F S of fixed points of a relatively nonexpansive mapping S, and the set T−10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems ...

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the ...