A NOTE ON X-log CONVEXITY IN Rn.

We define and look into the fundamental features of X-log convex, X-log quasi convex, X-log semi-strictly quasi convex, and X-log-pseudo convex functions. This paper provides several examples and arguments in favour of the concept. Also, we develope another X-log convex function as the sum of an X-log convex and X-log affine convex function. Additionally, we define local and global log-minimum. Under one condition, it is possible to demonstrate that the local log-minimum of an X-log convex and X-log quasi-convex function is also the global log-minimum. [ABSTRACT FROM AUTHOR]