In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These res...In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.展开更多
In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （...In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.展开更多
By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-...By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz maps are also obtained. These results generalize Rohde’s theorem in ? n and improve Balogh’s corresponding results in Carnot groups.展开更多
In this work,some new fixed point results for generalized Lipschitz mappings on generalized c-distance in cone b-metric spaces over Banach algebras are obtained,not acquiring the condition that the underlying cone sho...In this work,some new fixed point results for generalized Lipschitz mappings on generalized c-distance in cone b-metric spaces over Banach algebras are obtained,not acquiring the condition that the underlying cone should be normal or the mappings should be continuous.Furthermore,the existence and the uniqueness of the fixed point are proven for such mappings.These results greatly improve and generalize several well-known comparable results in the literature.Moreover,some examples and an application are given to support our new results.展开更多
基金Supported by the Foundation of Education Ministry of Hubei Province(D20102502)
文摘In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.
文摘In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.
文摘By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz maps are also obtained. These results generalize Rohde’s theorem in ? n and improve Balogh’s corresponding results in Carnot groups.
基金partially supported by the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities'Association(grant No.202101BA070001-045).
文摘In this work,some new fixed point results for generalized Lipschitz mappings on generalized c-distance in cone b-metric spaces over Banach algebras are obtained,not acquiring the condition that the underlying cone should be normal or the mappings should be continuous.Furthermore,the existence and the uniqueness of the fixed point are proven for such mappings.These results greatly improve and generalize several well-known comparable results in the literature.Moreover,some examples and an application are given to support our new results.
