The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Poom Kumam - One of the best experts on this subject based on the ideXlab platform.
-
relaxed inertial tseng s type method for solving the inclusion problem with application to image restoration
Mathematics, 2020Co-Authors: Jamilu Abubakar, Poom Kumam, Abdulkarim Hassan Ibrahim, Anantachai PadcharoenAbstract:The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally Monotone Mapping and a Monotone Mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving Monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods.
-
Viscosity approximation methods for Monotone Mappings and a countable family of nonexpansive Mappings
Mathematica Slovaca, 2011Co-Authors: Poom Kumam, Somyot PlubtiengAbstract:We use viscosity approximation methods to obtain strong convergence to common fixed points of Monotone Mappings and a countable family of nonexpansive Mappings. Let C be a nonempty closed convex subset of a Hilbert space H and P C is a metric projection. We consider the iteration process {x n } of C defined by x 1 = x ∈ C is arbitrary and $$ x_{n + 1} = \alpha _n f(x_n ) + (1 - \alpha _n )S_n P_C (x_n + \lambda _n Ax_n ) $$ where f is a contraction on C, {S n } is a sequence of nonexpansive self-Mappings of a closed convex subset C of H, and A is an inverse-strongly-Monotone Mapping of C into H. It is shown that {x n } converges strongly to a common element of the set of common fixed points of a countable family of nonexpansive Mappings and the set of solutions of the variational inequality for an inverse-strongly-Monotone Mapping which solves some variational inequality. Finally, the ideas of our results are applied to find a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem, a zero of a maximal Monotone operator and a strictly pseudocontractive Mapping in a real Hilbert space. The results of this paper extend and improve the results of Chen, Zhang and Fan.
-
weak convergence theorem for Monotone Mappings and a countable family of nonexpansive Mappings
Journal of Computational and Applied Mathematics, 2009Co-Authors: Somyot Plubtieng, Poom KumamAbstract:In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive Mappings and the set of solutions of the variational inequality problem for an @a-inverse-strongly-Monotone Mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a Monotone Mapping.
-
a hybrid approximation method for equilibrium and fixed point problems for a Monotone Mapping and a nonexpansive Mapping
Nonlinear Analysis: Hybrid Systems, 2008Co-Authors: Poom KumamAbstract:The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive Mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly Monotone Mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal Monotone operator and a strictly pseudocontractive Mapping in a real Hilbert space.
Somyot Plubtieng - One of the best experts on this subject based on the ideXlab platform.
-
Existence and Algorithm for Generalized Mixed Equilibrium Problem with a Relaxed Monotone Mapping
Thai Journal of Mathematics, 2015Co-Authors: Prapairat Junlouchai, Somyot PlubtiengAbstract:In this paper, we introduce a new generalized mixed equilibrium problem with a relaxed Monotone Mapping.By using KKM theorem, we establish an existence theorem for this problem in a Hausdorff topological vector space.Moreover, we introduce an iterative sequence and prove a weak convergence theorem for a generalized mixed equilibriumproblem with a relaxed Monotone Mapping in Hilbert spaces. The results presented in this paper can be viewed asgeneralization and extension of many results in literature.
-
The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping
Abstract and Applied Analysis, 2014Co-Authors: Phayap Katchang, Somyot PlubtiengAbstract:We modify the three-step iterative schemes to prove the strong convergence theorems by using the hybrid projection methods for finding a common element of the set of solutions of fixed points for a pseudocontractive Mapping and a nonexpansive semigroup Mapping and the set of solutions of a variational inequality problem for a Monotone Mapping in a Hilbert space under some appropriate control conditions. Our theorems extend and unify most of the results that have been proved for this class of nonlinear Mappings.
-
when a vector quasiMonotone Mapping is a vector Monotone Mapping
Optimization Letters, 2014Co-Authors: A P Farajzadeh, Somyot PlubtiengAbstract:In this paper we provide a sufficient conditions that under them a vector quasiMonotone set-valued Mapping transfer to a vector Monotone set-valued Mapping. In fact this note is a vector version of the papers (Farajzadeh, J Ineq Appl 2012:192, 2012) and (Hadjisavvas, Appl Math Lett 19:913–915, 2006).
-
Viscosity approximation methods for Monotone Mappings and a countable family of nonexpansive Mappings
Mathematica Slovaca, 2011Co-Authors: Poom Kumam, Somyot PlubtiengAbstract:We use viscosity approximation methods to obtain strong convergence to common fixed points of Monotone Mappings and a countable family of nonexpansive Mappings. Let C be a nonempty closed convex subset of a Hilbert space H and P C is a metric projection. We consider the iteration process {x n } of C defined by x 1 = x ∈ C is arbitrary and $$ x_{n + 1} = \alpha _n f(x_n ) + (1 - \alpha _n )S_n P_C (x_n + \lambda _n Ax_n ) $$ where f is a contraction on C, {S n } is a sequence of nonexpansive self-Mappings of a closed convex subset C of H, and A is an inverse-strongly-Monotone Mapping of C into H. It is shown that {x n } converges strongly to a common element of the set of common fixed points of a countable family of nonexpansive Mappings and the set of solutions of the variational inequality for an inverse-strongly-Monotone Mapping which solves some variational inequality. Finally, the ideas of our results are applied to find a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem, a zero of a maximal Monotone operator and a strictly pseudocontractive Mapping in a real Hilbert space. The results of this paper extend and improve the results of Chen, Zhang and Fan.
-
weak convergence theorem for Monotone Mappings and a countable family of nonexpansive Mappings
Journal of Computational and Applied Mathematics, 2009Co-Authors: Somyot Plubtieng, Poom KumamAbstract:In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive Mappings and the set of solutions of the variational inequality problem for an @a-inverse-strongly-Monotone Mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a Monotone Mapping.
Naseer Shahzad - One of the best experts on this subject based on the ideXlab platform.
-
a scheme for a solution of a variational inequality for a Monotone Mapping and a fixed point of a pseudocontractive Mapping
Journal of Inequalities and Applications, 2015Co-Authors: Mohammed A Alghamdi, Naseer Shahzad, Habtu ZegeyeAbstract:We introduce an iterative process which converges strongly to a common point of the solution set of a variational inequality problem for a Lipschitzian Monotone Mapping and the fixed point set of a continuous pseudocontractive Mapping in Hilbert spaces. In addition, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
-
minimum norm solution of variational inequality and fixed point problem in banach spaces
Optimization, 2015Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:Abstract We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an -inverse strongly Monotone Mapping and a fixed point of relatively non-expansive Mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-linear operators.
-
approximating a common point of fixed points of a pseudocontractive Mapping and zeros of sum of Monotone Mappings
Fixed Point Theory and Applications, 2014Co-Authors: Naseer Shahzad, Habtu ZegeyeAbstract:Let C be a closed and convex subset of a real Hilbert space H. Let T be a Lipschitzian pseudocontractive Mapping of C into itself, A be a γ-inverse strongly Monotone Mapping of C into H and let B be a maximal Monotone operator on H such that the domain of B is included in C. We introduce an iteration scheme for finding a minimum-norm point of F ( T ) ∩ ( A + B ) − 1 ( 0 ) . Application to a common element of the set of fixed points of a Lipschitzian pseudocontractive and solutions of variational inequality for α-inverse strongly Monotone Mappings is included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear Mappings. To the best of our knowledge, approximating a common fixed point of pseudocontractive Mappings with explicit scheme has not been possible and our result is even the first result that states the solution of a variational inequality in the set of fixed points of pseudocontractive Mappings. Our scheme which is explicit is the best to use for the problem under consideration.
-
Strong convergence of an iterative method for pseudo-contractive and Monotone Mappings
Journal of Global Optimization, 2011Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive Mapping and solutions of variational inequality problem for Monotone Mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive Mappings and solutions set of finite family of variational inequality problems for continuous Monotone Mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear Mappings.
-
Strong convergence theorems for Monotone Mappings and relatively weak nonexpansive Mappings
Nonlinear Analysis: Theory Methods & Applications, 2009Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:In this paper, we prove strong convergence theorems to a zero of Monotone Mapping and a fixed point of relatively weak nonexpansive Mapping. Moreover, strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive Mapping and a solution of a certain variational problem are proved under appropriate conditions.
Habtu Zegeye - One of the best experts on this subject based on the ideXlab platform.
-
a scheme for a solution of a variational inequality for a Monotone Mapping and a fixed point of a pseudocontractive Mapping
Journal of Inequalities and Applications, 2015Co-Authors: Mohammed A Alghamdi, Naseer Shahzad, Habtu ZegeyeAbstract:We introduce an iterative process which converges strongly to a common point of the solution set of a variational inequality problem for a Lipschitzian Monotone Mapping and the fixed point set of a continuous pseudocontractive Mapping in Hilbert spaces. In addition, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
-
minimum norm solution of variational inequality and fixed point problem in banach spaces
Optimization, 2015Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:Abstract We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an -inverse strongly Monotone Mapping and a fixed point of relatively non-expansive Mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-linear operators.
-
approximating a common point of fixed points of a pseudocontractive Mapping and zeros of sum of Monotone Mappings
Fixed Point Theory and Applications, 2014Co-Authors: Naseer Shahzad, Habtu ZegeyeAbstract:Let C be a closed and convex subset of a real Hilbert space H. Let T be a Lipschitzian pseudocontractive Mapping of C into itself, A be a γ-inverse strongly Monotone Mapping of C into H and let B be a maximal Monotone operator on H such that the domain of B is included in C. We introduce an iteration scheme for finding a minimum-norm point of F ( T ) ∩ ( A + B ) − 1 ( 0 ) . Application to a common element of the set of fixed points of a Lipschitzian pseudocontractive and solutions of variational inequality for α-inverse strongly Monotone Mappings is included. Our theorems improve and unify most of the results that have been proved in this direction for this important class of nonlinear Mappings. To the best of our knowledge, approximating a common fixed point of pseudocontractive Mappings with explicit scheme has not been possible and our result is even the first result that states the solution of a variational inequality in the set of fixed points of pseudocontractive Mappings. Our scheme which is explicit is the best to use for the problem under consideration.
-
Strong convergence of an iterative method for pseudo-contractive and Monotone Mappings
Journal of Global Optimization, 2011Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:In this paper, we introduce an iterative process which converges strongly to a common element of fixed points of pseudo-contractive Mapping and solutions of variational inequality problem for Monotone Mapping. As a consequence, we provide an iteration scheme which converges strongly to a common element of set of fixed points of finite family continuous pseudo-contractive Mappings and solutions set of finite family of variational inequality problems for continuous Monotone Mappings. Our theorems extend and unify most of the results that have been proved for this class of nonlinear Mappings.
-
Strong convergence theorems for Monotone Mappings and relatively weak nonexpansive Mappings
Nonlinear Analysis: Theory Methods & Applications, 2009Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:In this paper, we prove strong convergence theorems to a zero of Monotone Mapping and a fixed point of relatively weak nonexpansive Mapping. Moreover, strong convergence theorems to a point which is a fixed point of relatively weak nonexpansive Mapping and a solution of a certain variational problem are proved under appropriate conditions.
Jinlin Guan - One of the best experts on this subject based on the ideXlab platform.
-
A System of Generalized Variational Inclusions Involving a New Monotone Mapping in Banach Spaces
Abstract and Applied Analysis, 2013Co-Authors: Jinlin GuanAbstract:We introduce a new Monotone Mapping in Banach spaces, which is an extension of the -Monotone Mapping studied by Nazemi (2012), and we generalize the variational inclusion involving the -Monotone Mapping. Based on the new Monotone Mapping, we propose a new proximal Mapping which combines the proximal Mapping studied by Nazemi (2012) with the Mapping studied by Lan et al. (2011) and show its Lipschitz continuity. Based on the new proximal Mapping, we give an iterative algorithm. Furthermore, we prove the convergence of iterative sequences generated by the algorithm under some appropriate conditions. Our results improve and extend corresponding ones announced by many others.