On a generalisation of Local Uniform Rotundity

On the Weak Uniform Rotundity of Banach Spaces

1. Definitions and preliminaries. In this note, X and Y denote Banach spaces and X∗ and Y∗ denote the conjugate spaces of X and Y , respectively. Let A⊂X be a closed subset and X/A denote the quotient space. We use S(X) for the unit sphere in X and Plp (Xi) for the lp product space. We refer to [1, 3] for the following definitions and notations. For more recent treatment, one may see, for examp...

Influence of Non-Uniform Wall Temperature on Local Heat Transfer Coefficient in a Rotating Square Channel

 Abstract: This paper presents the results of an experimental examination of the effect of non-uniform wall temperature on local heat transfer coefficient in a rotating smooth-walled square channel. Three different thermal boundary situations were investigated: (a) even and odd (four) wall uniform temperature, (b) even and odd (four) wall uniform heat flux, and (c) even (leading and trailing) w...

On uniform Kadec-Klee properties and rotundity in generalized Cesàro sequence spaces

We consider the generalized Cesàro sequence spaces defined by Suantai (2003) and consider it equipped with the Amemiya norm. The main purpose of this paper is to show that ces (p) equipped with the Amemiya norm is rotund and has uniform Kadec-Klee property. 1. Introduction. In the whole paper, N and R stand for the sets of natural numbers and real numbers, respectively. Let (X, · ·) be a real n...

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Strong Rotundity and Optimization