SAMS Subject Classification Number: 33

Künzi and Yilzid introduced the concept of convexity structures in the sense of Takahashi in quasi-pseudometric spaces. In this talk, we continue the study of this theory, introducing the concept of \(W\)-convexity for real-valued pair of functions defined on an asymmetrically normed real vector space. Moreover, we show that all minimal pairs of functions defined on an asymmetrically normed real vector space equipped with a convex structure which is \(W\)-convex is translation-invariant.