Iterative algorithms for approximating solutions of some optimization problems in Hadamard spaces.

Masters Degree. University of KwaZulu-Natal, Durban.Abstract available in PDF.Some text in red

A new inertial condition on the subgradient extragradient method for solving pseudomonotone equilibrium problem

In this paper we study the pseudomonotone equilibrium problem. We consider a new inertial condition for the subgradient extragradient method with self-adaptive step size for approximating a solution of the equilibrium problem in a real Hilbert space. Our proposed method contains inertial factor with new conditions that only depend on the iteration coefficient. We obtain a weak convergence result of the proposed method under weaker conditions on the inertial factor than many existing conditions in the literature. Finally, we present some numerical experiments for our proposed method in comparison with existing methods in the literature. Our result improves, extends and generalizes several existing results in the literature

Implication of Mother’s Depression on Educational Development of Internally displaced Nigerian Children

This study examined the implication of the mother’s depression on educational development of the internally displaced children in four states in Nigeria. Correlational survey method was used to randomly sample 959 women and 706 children who were seeking refuge at IDP camps located in each of the four states participated in the study. Zung Depression Self-Rating Scale (1965) and numerical, verbal and visual reasoning tests developed by Bareet (2004) were used to measure mother’s depression and educational development of the children respectively. Pearson correlation was used to determine the relationship among the variables of study. Results show that, there was a negative correlation between the age of the mothers and sex of the children; a negative relationship existed between the age of the mother and their educational background; it further revealed that positive relationships were found between the mothers’ depression and educational background of the children; sex of the children correlated negatively and significantly with the mothers’ depression and, mothers’ depression was significantly related to numerical, verbal and visual reasoning tests. The study concluded that displacement has a capacity to provoke fear, helplessness, depression or awfulness in response to the threat of injury, molestation or death and affecting the fundamental care for the children educationally by their mothers.Key Words: Mother’s depression, educational development internally displaced, women, children, Nigeri

Fixed point approach for solving optimization problems in Hilbert, Banach and convex metric spaces.

Doctoral Degree. University of KwaZulu-Natal, Durban.In this thesis, we study the fixed point approach for solving optimization problems in real Hilbert, Banach and Hadamard spaces. These optimization problems include the variational inequality problem, split variational inequality problem, generalized variational inequality problem, split equality problem, monotone inclusion problem, split monotone inclusion problem, minimization problem, split equilibrium problem, among others. We consider some interesting classes of mappings such as the nonexpansive semigroup in real Hilbert spaces, strict pseudo-contractive mapping in real Hilbert spaces and 2-uniformly convex real Banach spaces, nonexpansive mapping between a Hilbert space and a Banach space, and quasi-pseudocontractive mapping in Hilbert spaces and Hadamard spaces. We introduce several iterative schemes for approximating the solutions of the various aforementioned optimization problems and fixed point problems and prove their convergence results. We adopt and implement several inertial methods such as the inertial-viscosity-type algorithm, relaxed inertial subgradient extragradient, modified inertial forward-backward splitting algorithm viscosity method, among others. Furthermore, we present several novel and practical applications of our results to solve other optimization problems, image restoration problem, among others. Finally we present several numerical examples in comparison with some results in the literature to illustrate the applicability of our proposed methods