This Article Examines a Class of Widespread Non-Linear Vector Inequalities and Nearly Variable Characters With Maps In Hausdorff's Topological Vector Space Areas Which Include Popular, Non-Linear, Mixed Variable Inequalities, Widespread, Mixed, Near-Variable Inequalities, Etc. We Obtain Solutions For Generalized, Nonlinear Non-Linear Vector Inequalities In Local, Convex, Topological Vector Spaces, Using a Fixed-Point Theorem.