Invariant means on almost periodic functions and fixed point properties

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Fixed Point Theory for Almost Convex Functions

New fixed and periodic point results on cone metric spaces

In this paper, several fixed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.

Vector-valued Means and Weakly Almost Periodic Functions

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...

On Hartman Almost Periodic Functions

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...