In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of th...In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].展开更多
The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real...The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.展开更多
Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K ...Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.展开更多
This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combi...This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.展开更多
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx...We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.展开更多
We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-st...We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.展开更多
In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation m...In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2].展开更多
Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point...In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.展开更多
This paper proposes a new rapid and efficient method for woolen textile simulation- mapping synthesize. This method uses a stochastic function to simulate fuzz on some types of wool textile. The wool yarns are simulat...This paper proposes a new rapid and efficient method for woolen textile simulation- mapping synthesize. This method uses a stochastic function to simulate fuzz on some types of wool textile. The wool yarns are simulated on the basis of Phong illumination model. In order to obtain a visual effect of the wool textile with fuzz, the light intensity of fuzz is synthesized as a color parameter in the Phong illumination model after the yams have been simulated. The model of woolen textile with fuzz can be built eventually.With synthesis mapping methods, user can choose his favorite fuzz density on the wool by controlling some appropriate parameters.展开更多
为了改善在动态场景下同步定位与地图绘制(Simultaneous Localization And Mapping,SLAM)算法定位精度低的问题,提出一种基于轻量化YOLOv(You Only Look Once version)8n的动态视觉SLAM算法。利用加权双向特征金字塔网络(Bidirectional ...为了改善在动态场景下同步定位与地图绘制(Simultaneous Localization And Mapping,SLAM)算法定位精度低的问题,提出一种基于轻量化YOLOv(You Only Look Once version)8n的动态视觉SLAM算法。利用加权双向特征金字塔网络(Bidirectional Feature Pyramid Network,BiFPN)对YOLOv8n模型进行轻量化改进,减少其参数量。在SLAM算法中引入轻量化YOLOv8n模型,并结合稀疏光流法组成目标检测线程,以去除动态特征点,利用经过筛选的特征点进行特征匹配和位姿估计。实验结果表明:轻量化YOLOv8n模型参数量下降了36.7%,权重减少了33.3%,能够实现YOLOv8n模型的轻量化;与ORB-SLAM3算法相比,所提算法在动态场景下的定位精度提高83.38%,有效提高了动态场景下SLAM算法的精度。展开更多
A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to...A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.展开更多
The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity d...The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.展开更多
基金the Thailand Research Fund for financial support under Grant BRG5280016
文摘In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].
基金Project supported by the National Natural Science Foundation of China(Nos.11172233,11302169,11302170,and 11472212)the Fundamental Research Funds for the Central Universities(No.3102014JCQ01079)
文摘The stochastic response of a noisy system with non-negative restoring force is investigated. The generalized cell mapping （GCM） method compute the transient and stationary probability density functions （PDFs） real-power is used to Combined with the global properties of the noise-free system, the evolutionary process of the tran- sient PDFs is revealed. The results show that stochastic P-bifurcation occurs when the system parameter varies in the response analysis and the stationary PDF evolves from bimodal to unimodal along the unstable manifold during the bifurcation.
文摘Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.
基金Supported by the National Natural Science Foundation of China(Nos.11172197,11332008 and 11572215)the Natural Science Foundation of Tianjin through a key-project Grant(12JCZDJC30400)the UC MEXUS-CONACy T through the project Hybridizing Set Oriented Methods and Evolutionary Strategies to Obtain Fast and Reliable Multi-objective Optimization Algorithms
文摘This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.
基金the Natural Science Foundation of China (No. 10471151)the Educational Science Foundation of Chongqing (KJ051307).
文摘We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.
文摘We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.
文摘In this paper, to find the fixed points of the nonexpansive nonself-mappings, we introduced two new viscosity approximation methods, and then we prove the iterative sequences defined by above viscosity approximation methods which converge strongly to the fixed points of nonexpansive nonself-mappings. The results presented in this paper extend and improve the results of Song-Chen [1] and Song-Li [2].
文摘Sufficient conditions are given to assert that two differentiable mappings between Banach spaces have common values. The proof is essentially based upon continuation methods.
文摘In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.
文摘This paper proposes a new rapid and efficient method for woolen textile simulation- mapping synthesize. This method uses a stochastic function to simulate fuzz on some types of wool textile. The wool yarns are simulated on the basis of Phong illumination model. In order to obtain a visual effect of the wool textile with fuzz, the light intensity of fuzz is synthesized as a color parameter in the Phong illumination model after the yams have been simulated. The model of woolen textile with fuzz can be built eventually.With synthesis mapping methods, user can choose his favorite fuzz density on the wool by controlling some appropriate parameters.
文摘为了改善在动态场景下同步定位与地图绘制(Simultaneous Localization And Mapping,SLAM)算法定位精度低的问题,提出一种基于轻量化YOLOv(You Only Look Once version)8n的动态视觉SLAM算法。利用加权双向特征金字塔网络(Bidirectional Feature Pyramid Network,BiFPN)对YOLOv8n模型进行轻量化改进,减少其参数量。在SLAM算法中引入轻量化YOLOv8n模型,并结合稀疏光流法组成目标检测线程,以去除动态特征点,利用经过筛选的特征点进行特征匹配和位姿估计。实验结果表明:轻量化YOLOv8n模型参数量下降了36.7%,权重减少了33.3%,能够实现YOLOv8n模型的轻量化;与ORB-SLAM3算法相比,所提算法在动态场景下的定位精度提高83.38%,有效提高了动态场景下SLAM算法的精度。
基金This work is partially supported by D.G.E.S. PB 96-1338-CO2-01 and the Junta de Andalucla.
文摘A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.
基金funded by the Natural Science Foundation Committee,China(41364001,41371435)
文摘The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.
