Several results are established about Banach spaces X which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from X to the Lebesgue-Bochner space L2(X) if and only if X is super-re exive. A basis characterization of the renorming property for dual Banach spaces is g...

In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak co...

In summability theory, de la Vallée-Poussin’s mean is first used to define the (V, λ)-summability by Leindler [9]. Malkowsky and Savaş [14] introduced and studied some sequence spaces which arise from the notion of generalized de la ValléePoussin mean. Also the (V, λ)-summable sequence spaces have been studied by many authors including [6] and [20]. Recently, there has been a lot of interest in...

In this paper, we first introduce a class of nonlinear mappings called generic generalized nonspreading which contains the class of generalized nonspreading mappings in a Banach space and then prove an attractive point theorem for such mappings in a Banach space. Furthermore, we prove a mean convergence theorem of Baillon’s type and a weak convergence theorem of Mann’s type for such nonlinear m...

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly uniformly continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Hervés and Vald...

In [1] Dhage, O’Regan and Agarwal introduced the class of weak isotone mappings and the class of countably condensing mappings in an ordered Banach space and they prove some common fixed point theorems for weak isotone mappings. In this paper we introduce the notion of g-weak isotone mappings which allows us to generalize some common fixed point theorems of [1]. We recall the definition of orde...

The Banach frame for a Banach space  can reconstruct each vector in  by the pre-frame operator or the reconstruction operator. The Banach Λ-frame for operator spaces was introduced by Kaushik, Vashisht and Khattar [Reconstruction Property and Frames in Banach Spaces, Palestine Journal of Mathematics, 3(1), 2014, 11-26]. In this paper we give necessary and sufficient conditions for the existen...

The main results of the paper: (1) The dual Banach space X∗ contains a linear subspace A ⊂ X∗ such that the set A of all limits of weak∗ convergent bounded nets in A is a proper norm-dense subset of X∗ if and only if X is a non-quasi-reflexive Banach space containing an infinite-dimensional subspace with separable dual. (2) Let X be a non-reflexive Banach space. Then there exists a convex subse...