scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
C. Izuchukwu ◽  
F. O. Isiogugu ◽  
C. C. Okeke
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Iteration Process ◽  
Point Theory ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Point Problem ◽  
Common Solution

Abstract In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.

scholarly journals STRONG CONVERGENCE OF A NEW HYBRID ALGORITHM FOR FIXED POINT PROBLEMS AND EQUILIBRIUM PROBLEMS

2018 ◽  
Vol 24 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hybrid Algorithm ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Mann Iteration ◽  
Common Solution ◽  
Mild Conditions

The paper considers the problem of finding a common solution of a pseudomonotone and Lipschitz-type equilibrium problem and a fixed point problem for a quasi nonexpansive mapping in a Hilbert space. A new hybrid algorithm is introduced for approximating a solution of this problem. The presented algorithm can be considered as a combination of the extragradient method (two-step proximal-like method) and a modified version of the normal Mann iteration. It is well known that the normal Mann iteration has the weak convergence, but in this paper we has obtained the strong convergence of the new algorithm under some mild conditions on parameters. Several numerical experiments are reported to illustrate the convergence of the algorithm and also to show the advantages of it over existing methods.

scholarly journals Strong convergence theorem for family of minimization and monotone inclusion problems in Hadamard spaces

2021 ◽  
Vol 40 (2) ◽  
pp. 525-559
Author(s):  
Chinedu Izuchukwu ◽  
Godwin C. Ugwunnadi ◽  
Oluwatosin Temitope Mewomo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Minimization Problem ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Inclusion Problem ◽  
Point Problem ◽  
Monotone Inclusion ◽  
Common Solution ◽  
Monotone Inclusion Problem

In this paper, we introduce a modified Ishikawa-type proximal point algorithm for approximating a common solution of minimization problem, monotone inclusion problem and fixed point problem. We obtain a strong convergence of the proposed algorithm to a common solution of finite family of minimization problem, finite family of monotone inclusion problem and fixed point problem for asymptotically demicontractive mapping in Hadamard spaces. Numerical example is given to illustrate the applicability of our main result. Our results complement and extend some recent results in literature.

scholarly journals Iterative approximations with hybrid techniques for fixed points and equilibrium problems

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1997-2009
Author(s):  
Afrah Abdou ◽  
Badriah Alamri ◽  
Yeol Cho ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Hybrid Techniques ◽  
Contractive Mappings ◽  
Generalized Equilibrium

In this paper, we consider an iterative algorithm by using the shrinking projection method for solving the fixed point problem of the pseudo-contractive mappings and the generalized equilibrium problems. We prove some lemmas for our main result and a strong convergence theorem for the proposed algorithm.

A viscosity-type proximal point algorithm for monotone equilibrium problem and fixed point problem in an Hadamard space

2020 ◽  
pp. 2150058
Author(s):  
K. O. Aremu ◽  
C. Izuchukwu ◽  
A. A. Mebawondu ◽  
O. T. Mewomo
Keyword(s):  
Fixed Point ◽  
Proximal Point Algorithm ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Feasibility Problem ◽  
Point Problem ◽  
Hadamard Space ◽  
Proximal Point ◽  
Common Solution

In this paper, we introduce a viscosity-type proximal point algorithm comprising of a finite composition of resolvents of monotone bifunctions and a generalized asymptotically nonspreading mapping recently introduced by Phuengrattana [Appl. Gen. Topol. 18 (2017) 117–129]. We establish a strong convergence result of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a generalized asymptotically nonspreading and nonexpansive mappings, which is also a unique solution of some variational inequality problems in an Hadamard space. We apply our result to solve convex feasibility problem and to approximate a common solution of a finite family of minimization problems in an Hadamard space.

scholarly journals Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 255
Author(s):  
Yan Tang ◽  
Yeol Cho
Keyword(s):  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Point Problem ◽  
Step Size ◽  
Convergence Theorems ◽  
Common Solution ◽  
Variational Inclusion Problem

In this paper, the split variational inclusion problem (SVIP) and the system of equilibrium problems (EP) are considered in Hilbert spaces. Inspired by the works of Byrne et al., López et al., Moudafi and Thukur, Sobumt and Plubtieng, Sitthithakerngkiet et al. and Eslamian and Fakhri, a new self-adaptive step size algorithm is proposed to find a common element of the solution set of the problems SVIP and EP. Convergence theorems are established under suitable conditions for the algorithm and application to the common solution of the fixed point problem, and the split convex optimization problem is considered. Finally, the performances and computational experiments are presented and a comparison with the related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

scholarly journals Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasir Arfat ◽  
Poom Kumam ◽  
Parinya Sa Ngiamsunthorn ◽  
Muhammad Aqeel Ahmad Khan ◽  
Hammad Sarwar ◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Common Solution ◽  
Theoretical Results

Abstract In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

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