The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Jenchih Yao - One of the best experts on this subject based on the ideXlab platform.
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further generalized Contraction Mapping principle and best proximity theorem in metric spaces
Fixed Point Theory and Applications, 2015Co-Authors: Jenchih YaoAbstract:The aim of this paper is to prove a more generalized Contraction Mapping principle. By using this more generalized Contraction Mapping principle, a further generalized best proximity theorem was established. Some concrete results have been derived by using the above two theorems. The results of this paper improve many important results published recently in the literature.
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generalized Contraction Mapping principle and generalized best proximity point theorems in probabilistic metric spaces
Fixed Point Theory and Applications, 2015Co-Authors: Wenbiao Gao, Jenchih YaoAbstract:The purpose of this paper is to introduce some basic definitions about fixed point and best proximity point in two classes of probabilistic metric spaces and to prove Contraction Mapping principle and relevant best proximity point theorems. The first class is the so-called S-probabilistic metric spaces. In S-probabilistic metric spaces, the generalized Contraction Mapping principle and generalized best proximity point theorems have been proved by authors. These results improve and extend the recent results of Su and Zhang (Fixed Point Theory Appl. 2014:170, 2014). The second class is the so-called Menger probabilistic metric spaces. In Menger probabilistic metric spaces, the Contraction Mapping principle and relevant best proximity point theorems have been proved by authors. These results also improve and extend the results of many authors. In order to get the results of this paper, some new methods have been used. Meanwhile some error estimate inequalities have been established.
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ishikawa iterative algorithms for a generalized equilibrium problem and fixed point problems of a pseudo Contraction Mapping
Journal of Global Optimization, 2010Co-Authors: Jianwen Peng, Jenchih YaoAbstract:In this paper, we propose two Ishikawa iterative algorithms for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a Lipschitz continuous pseudo-Contraction Mapping. We obtain both strong convergence theorems and weak convergence theorems in a Hilbert space.
Wutiphol Sintunavarat - One of the best experts on this subject based on the ideXlab platform.
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ulam hyers stability and well posedness of fixed point problems for α λ Contraction Mapping in metric spaces
Abstract and Applied Analysis, 2014Co-Authors: Marwan Amin Kutbi, Wutiphol SintunavaratAbstract:We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized Contraction Mapping, so called --Contraction Mapping. The results in this paper generalize and unify several results in the literature such as the Banach Contraction principle.
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generalized ulam hyers stability well posedness and limit shadowing of fixed point problems for α β Contraction Mapping in metric spaces
The Scientific World Journal, 2014Co-Authors: Wutiphol SintunavaratAbstract:We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized Contraction Mapping, the so-called α-β-Contraction Mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach Contraction principle.
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common fixed point theorem for hybrid generalized multi valued Contraction Mappings
Applied Mathematics Letters, 2012Co-Authors: Wutiphol Sintunavarat, Poom KumamAbstract:Abstract In this paper, we extend a multi-valued Contraction Mapping to a cyclic multi-valued Contraction Mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued Contraction Mapping. Our results extend, generalize and unify Nadler’s multi-valued Contraction Mapping and many fixed point theorems for multi-valued Mappings.
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Common fixed point theorem for cyclic generalized multi-valued Contraction Mappings
Applied Mathematics Letters, 2012Co-Authors: Wutiphol Sintunavarat, Poom KumamAbstract:AbstractIn this paper, we extend a multi-valued Contraction Mapping to a cyclic multi-valued Contraction Mapping. We also establish the existence of common fixed point theorem for a cyclic multi-valued Contraction Mapping. Our results extend, generalize and unify Nadler’s multi-valued Contraction Mapping and many fixed point theorems for multi-valued Mappings
Kai-yuan Cai - One of the best experts on this subject based on the ideXlab platform.
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Repetitive Control with Nonlinear Systems: A Contraction Mapping Method
Filtered Repetitive Control with Nonlinear Systems, 2019Co-Authors: Quan Quan, Kai-yuan CaiAbstract:The adaptive-control-like method utilizes Lyapunov-based design techniques to develop feedforward to compensate for unknown disturbance. Moreover, the designed controllers depend on the concrete forms of the Lyapunov functions. The Lyapunov-based design technique is a good choice for nonlinear RC problems. However, in most cases, no general method exists for constructing Lyapunov functions for ordinary problems. Contraction Mapping is a widely used tool for iterative learning control (ILC, or iterative learning controller, which is also designated as ILC). Using this tool, the ILC design is straightforward and uniform without requiring Lyapunov functions. Inspired by this concept, a Contraction Mapping-based RC design is proposed for a class of nonlinear systems in this chapter.
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Saturated repetitive control for a class of nonlinear systems: A Contraction Mapping method
Systems & Control Letters, 2018Co-Authors: Quan Quan, Kai-yuan CaiAbstract:Abstract Contraction Mapping methods do not need to know about the concrete form of plant models like the Lyapunov method. This is the biggest advantage over other methods in the field of iterative learning control for example. However, it is difficult to use such a tool to analyze repetitive control systems. This paper proposes a Contraction Mapping method based on spectral theory to design a saturated repetitive controller for a class of nonlinear systems, where the derived necessary and sufficient condition on the spectral radius can reduce the conservatism as much as possible. The feasibility of our work is demonstrated through a robotic manipulator tracking example.
Marwan Amin Kutbi - One of the best experts on this subject based on the ideXlab platform.
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ulam hyers stability and well posedness of fixed point problems for α λ Contraction Mapping in metric spaces
Abstract and Applied Analysis, 2014Co-Authors: Marwan Amin Kutbi, Wutiphol SintunavaratAbstract:We study Ulam-Hyers stability and the well-posedness of the fixed point problem for new type of generalized Contraction Mapping, so called --Contraction Mapping. The results in this paper generalize and unify several results in the literature such as the Banach Contraction principle.
Karl Schmedders - One of the best experts on this subject based on the ideXlab platform.
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discrete time dynamic principal agent models Contraction Mapping theorem and computational treatment
Quantitative Economics, 2020Co-Authors: Philipp Renner, Karl SchmeddersAbstract:We consider discrete‐time dynamic principal–agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a Contraction Mapping theorem and so also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal–agent problems at each iteration. As a result, in the discrete‐time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi‐level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal–agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature. Optimal unemployment tax principal–agent model repeated moral hazard C63 D80 D82
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Discrete‐time dynamic principal–agent models: Contraction Mapping theorem and computational treatment
Quantitative Economics, 2020Co-Authors: Philipp Renner, Karl SchmeddersAbstract:We consider discrete‐time dynamic principal–agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a Contraction Mapping theorem and so also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal–agent problems at each iteration. As a result, in the discrete‐time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi‐level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal–agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature. Optimal unemployment tax principal–agent model repeated moral hazard C63 D80 D82
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Discrete‐time dynamic principal–agent models: Contraction Mapping theorem and computational treatment
Quantitative Economics, 2020Co-Authors: Philipp Renner, Karl SchmeddersAbstract:We consider discrete‐time dynamic principal–agent problems with continuous choice sets and potentially multiple agents. We prove the existence of a unique solution for the principal's value function only assuming continuity of the functions and compactness of the choice sets. We do this by a Contraction Mapping theorem and so also obtain a convergence result for the value function iteration. To numerically compute a solution for the problem, we have to solve a collection of static principal–agent problems at each iteration. As a result, in the discrete‐time setting solving the static problem is the difficult step. If the agent's expected utility is a rational function of his action, then we can transform the bi‐level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal–agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.