Zabidin Salleh

Pairwise Weakly Regular-Lindelöf Spaces

We will introduce and study the pairwise weakly regular-Lindelof bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelof subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regular-Lindelof property is not a hereditary property. Some counterexamples will be considered in order to establish some of their relations.

Modification of Nonlinear Conjugate Gradient Method with Weak Wolfe-Powell Line Search

Conjugate gradient (CG) method is used to find the optimum solution for the large scale unconstrained optimization problems. Based on its simple algorithm, low memory requirement, and the speed of obtaining the solution, this method is widely used in many fields, such as engineering, computer science, and medical science. In this paper, we modified CG method to achieve the global convergence with various line searches. In addition, it passes the sufficient descent condition without any line search. The numerical computations under weak Wolfe-Powell line search shows that the efficiency of the new method is superior to other conventional methods.

Some results on (δ-pre, s)-continuous functions

We study some properties of (δ-pre, s)-continuous functions. Basic characterizations and several properties concerning (δ-pre, s)-continuous functions are studied. The general cases for the composition of functions under specific conditions which yield (δ-pre, s)-continuous functions are also studied and we obtained some results.