Common solution for a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces

2020 ◽  
Vol 114 (2) ◽  
Author(s):  
Shih-sen Chang ◽  
L. Wang ◽  
X. R. Wang ◽  
L. C. Zhao
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Point Problem ◽  
Common Solution ◽  
Demicontractive Mappings

scholarly journals New Iteration Scheme for Approximating a Common Fixed Point of a Finite Family of Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
F. O. Isiogugu ◽  
C. Izuchukwu ◽  
C. C. Okeke
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Real Hilbert Space ◽  
Fixed Point Problem ◽  
Iteration Scheme ◽  
Finite Family ◽  
Point Problem ◽  
Ongoing Research ◽  
Common Solution ◽  
Demicontractive Mappings

We introduce a new algorithm (horizontal algorithm) in a real Hilbert space, for approximating a common fixed point of a finite family of mappings, without imposing on the finite family of the control sequences ςnin=1∞i=1N, the condition that ∑i=1Nςni=1, for each n≥1. Furthermore, under appropriate conditions, the horizontal algorithm converges both weakly and strongly to a common fixed point of a finite family of type-one demicontractive mappings. It is also applied to obtain some new algorithms for approximating a common solution of an equilibrium problem and the fixed point problem for a finite family of mappings. Our work is a contribution to ongoing research on iteration schemes for approximating a common solution of fixed point problems of a finite family of mappings and equilibrium problems.

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 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.

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 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 A Self-Adaptive Algorithm for the Common Solution of the Split Minimization Problem and the Fixed Point Problem

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 109
Author(s):  
Nattakarn Kaewyong ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Point ◽  
Minimization Problem ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Step Size ◽  
Common Solution ◽  
And Performance ◽  
Self Adaptive

In this paper, a new self-adaptive step size algorithm to approximate the solution of the split minimization problem and the fixed point problem of nonexpansive mappings was constructed, which combined the proximal algorithm and a modified Mann’s iterative method with the inertial extrapolation. The strong convergence theorem was provided in the framework of Hilbert spaces and then proven under some suitable conditions. Our result improved related results in the literature. Moreover, some numerical experiments were also provided to show our algorithm’s consistency, accuracy, and performance compared to the existing algorithms in the literature.

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