In this paper, we introduce two concepts of weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in Banach spaces. Then we obtain some results of the solutions existence for a system of vector variational-like inequalities with weakly relaxed ${eta_gamma-alpha_gamma}_{gamma in Gamma}$ pseudomonotone and demipseudomonotone mappings in reflexive...

The first part of the paper is devoted to metric characterizations of Banach spaces with no cotype and no type > 1 in terms of graphs with uniformly bounded degrees. In the second part we prove that Banach spaces containing bilipschitz images of the infinite diamond do not have the RadonNikodým property and give a new proof of the Cheeger-Kleiner result on Banach spaces containing bilipschitz i...

This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special ...

In this paper, we give characterizations of Riesz bases and near Riesz bases in Banach spaces. The notion of atomic system is defined and a characterization of atomic system has been given. Also results exhibiting relationship between frames, atomic systems and Riesz bases have been proved. Further, we show that every atomic system is a projection of a Riesz basis in Banach spaces. Finally, we ...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...

We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided L-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-I...

vol. 162, No. 2, 1991 k-β and k-Nearly Uniformly Convex Banach Spaces Denka Kutzarova Different uniform geometrical properties have been defined between the uniform convexity and the reflexivity of Banach spaces. In the present paper we introduce other properties of this type, namely k-β and k-nearly uniform convexity. The definitions, as well as some of the results presented here, are announce...

We consider proximinality and transitivity of proximinality for subspaces of finite codimen-sion in generalized direct sums of Banach spaces. We give several examples of Banach spaces where proximinality is transitive among subspaces of finite codimension. 1. Introduction. Let X be a Banach space and let Y be a closed subspace of X. We recall that Y is said to be a proximinal subspace of X if f...