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 viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space

2019 ◽  
Vol 20 (1) ◽  
pp. 193 ◽  
Author(s):  
C. Izuchukwu ◽  
K. O. Aremu ◽  
A. A. Mebawondu ◽  
O. T. Mewomo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Optimization Problems ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Hadamard Space ◽  
Proximal Point ◽  
Common Solution ◽  
Finite Sum ◽  
Monotone Bifunctions

<p>The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces.</p>

scholarly journals MODIFIED PROXIMAL POINT ALGORITHM FOR MINIMIZATION AND FIXED POINT PROBLEM IN CAT(0) SPACES

2021 ◽  
Vol 7 (1) ◽  
pp. 109
Author(s):  
Godwin Chidi Ugwunnadi
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Proximal Point Algorithm ◽  
Continuous Mapping ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Proximal Point ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Lower Semi

In this paper, we study modified-type proximal point algorithm for approximating a common solution of a lower semi-continuous mapping and fixed point of total asymptotically nonexpansive mapping in complete CAT(0) spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved.

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 On the proximal point algorithm and demimetric mappings in CAT(0) spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 277-294 ◽  
Author(s):  
Kazeem O. Aremu ◽  
Chinedu Izuchukwu ◽  
Godwin C. Ugwunnadi ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Proximal Point Algorithm ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Proximal Point ◽  
Numerical Example ◽  
Common Solution ◽  
Minimization Problems

Abstract In this paper, we introduce and study the class of demimetric mappings in CAT(0) spaces.We then propose a modified proximal point algorithm for approximating a common solution of a finite family of minimization problems and fixed point problems in CAT(0) spaces. Furthermore,we establish strong convergence of the proposed algorithm to a common solution of a finite family of minimization problems and fixed point problems for a finite family of demimetric mappings in complete CAT(0) spaces. A numerical example which illustrates the applicability of our proposed algorithm is also given. Our results improve and extend some recent results in the literature.

scholarly journals Multiple-sets split feasibility problem and split equality fixed point problem for firmly quasi-nonexpansive or nonexpansive mappings

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tongxin Xu ◽  
Luoyi Shi
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Fixed Point Problem ◽  
Feasibility Problem ◽  
Point Problem ◽  
Projection Operators ◽  
Nonexpansive Operators ◽  
Split Feasibility

AbstractIn this paper, we propose a new iterative algorithm for solving the multiple-sets split feasibility problem (MSSFP for short) and the split equality fixed point problem (SEFPP for short) with firmly quasi-nonexpansive operators or nonexpansive operators in real Hilbert spaces. Under mild conditions, we prove strong convergence theorems for the algorithm by using the projection method and the properties of projection operators. The result improves and extends the corresponding ones announced by some others in the earlier and recent 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.

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