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Journal of Convex Analysis 28 (2021), No. 1, 123--142
Copyright Heldermann Verlag 2021

Strictly Stable Generalized Monotone Maps and Two Versions of Wald's Axiom

Phan Thanh An
Faculty of Applied Science, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet, and: Vietnam National University Ho Chi Minh City, Linh Trung Ward,
Thu Duc District, Ho Chi Minh City, Vietnam, and: South Ural State University, Chelyabinsk, Russia

Vuong Thi Thao Binh
Faculty of Basic Sciences, Foreign Trade University, Hanoi, Vietnam

Nguyen Ngoc Hai
Department of Mathematics, Vietnam National University, Ho Chi Minh City, Vietnam

We consider the stable generalization of monotone maps in normed spaces. A dense subclass of s-quasimonotone maps, namely strictly s-quasimonotone maps, is introduced. For a differentiable map, strict s-quasimonotonicity of the gradient is equivalent to strict s-quasiconvexity of the underlying function. Some necessary and sufficient conditions of these maps are presented. Uses of these generalized convexity and generalized monotonicity in economics are considered. In particular, we investigate excess demand maps F in Rn satisfying a strong version of Wald's axiom and its weaker version on a convex cone (i.e., -F is s-quasimonotone).

Keywords: Excess demand, generalized monotonicity, density in normed spaces, s-quasimonotonicity, stability, strong version of Wald's axiom.

MSC: 26A51, 26B25; 52A41, 90C26.

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