We introduce some new classes of preinvex and invex functions, which are called ϕ-preinvex and ϕ-invex functions. We study some properties of these classes of ϕ-preinvex (ϕ-invex) functions. In particular, we establish the equivalence among the ϕ-preinvex functions, ϕ-invex functions, and ϕη-monotonicity of their differential under some suitable conditions.

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