In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an...In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.展开更多
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2....In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.展开更多
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
基金supported in part by National Natural Science Foundation of China (Grant No.10971167)
文摘In this paper,we give a reverse analog of the Bonnesen-style inequality of a convex domain in the surface X of constant curvature,that is,an isoperimetric deficit upper bound of the convex domain in X.The result is an analogue of the known Bottema's result of 1933 in the Euclidean plane E2.
文摘In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
