In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Furth...In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.展开更多
LetD be a disc with radiusr in the Euclidean plane ?2, and letF be a Lipschitz continuous real valued function onD. SupposeA 1 A 21 A 3 A 4 is an isosceles trapezoid with lengths of edges not greater thanr, and ∠A 1 ...LetD be a disc with radiusr in the Euclidean plane ?2, and letF be a Lipschitz continuous real valued function onD. SupposeA 1 A 21 A 3 A 4 is an isosceles trapezoid with lengths of edges not greater thanr, and ∠A 1 A 21 A 3 = α≤π/2 By means of the Brouwer fixed point theorem, it is proved that ifF has a Lipschitz constant λ≤min{1, tgα}, then there exist four coplanar points in the surfaceM = {(x, y, F(x, y))∈?3:(x, y)?} which span a tetragon congruent toA 1 A 21 A 3 A 4. In addition, some further problems are discussed.展开更多
文摘In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19231201)
文摘LetD be a disc with radiusr in the Euclidean plane ?2, and letF be a Lipschitz continuous real valued function onD. SupposeA 1 A 21 A 3 A 4 is an isosceles trapezoid with lengths of edges not greater thanr, and ∠A 1 A 21 A 3 = α≤π/2 By means of the Brouwer fixed point theorem, it is proved that ifF has a Lipschitz constant λ≤min{1, tgα}, then there exist four coplanar points in the surfaceM = {(x, y, F(x, y))∈?3:(x, y)?} which span a tetragon congruent toA 1 A 21 A 3 A 4. In addition, some further problems are discussed.
