Some problem on vector variational- like inequalities

The summary theory for vector variational inequalities has found its use in several branches, whether applied sciences or pure. It gives a unifiet formula to understand and study a large amount of linear-non-linear mathematical issues. This thesis dealt with the study and discuss of some results for the solutions existed to mixed vector variational-like problems (for shortly, MVVLP). Firstly, a new MVVLP involving generalized monotone operator in Hausdorff topological linear spaces (for shortly, ) is introduced. By employing technique and using some relevant hypotheses on the considering non-linear mappings the existence of a result for a recent class of MVVLP in the setting of are presented. Secondly, new definition of invexity is called invex function and new idea of inequality variational and additional problems to vector of topology space are given. Finally, some results of nonstandard vector variational inequality in -spaces are generalized. The solutions provided in this study renew and make better some solutions to many researchers.