INERTIAL RELAXED TSENG METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACE

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the existing literature used are successfully weakened. The strong convergence of the proposed method to a minimum-norm solution of a variational inequality problem are established. Furthermore, we present an application and some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature.

A comparative study of estimators in multilevel linear models

Multilevel Models are widely used in organizational research, educational research, epidemiology, psychology, biology and medical fields. In this paper, we recommend the situations where Bootstrap procedures through Minimum Norm Quadratic Unbiased Estimator (MINQUE) can be extremely handy than that of Restricted Maximum Likelihood (REML) in multilevel level linear regression models. In our simulation study the bootstrap by means of MINQUE is superior to REML in conditions where normality does not hold. Moreover, the real data application also supports our findings in terms of accuracy of estimates and their standard errors.