Robust (M-) estimation in linear models generally involves statistical functional processes. For drawing statistical conclusions (in large samples), some (uniform) linear approximations are usually needed for such functionals. In this context, the role of Hadamard differentiability is critically examined in this dissertation. In particular, the concept of the second-order Hadamard differenti-ab...

In this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0,∞) × [0,∞) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical v...

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. The main concern of this manuscript is numerical methods for dissipative chaotic infinite dimensional dynamical systems that are able to capture the stationary statistical properties of the underlying dynamical systems. We first survey results on temporal and spatial approximations that enjoy the...

The main object of this paper is to introduce a new concept of weak statistically Cauchy sequence in a normed space. It is shown that in a reflexive space, weak statistically Cauchy sequences are the same as weakly statistically convergent sequences. Finally, weak statistical convergence has been discussed in l p spaces. under the Creative Commons Attribution License, which permits unrestricted...

The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. Mathematics Subject Classification: 54E05, 03F60