Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces

In this paper, a new accelerated extrapolation Krasnoselski-Mann type algorithm for finding common element in the solution set of the hierarchical fixed point and split monotone variational inclusion problems are introduced in the setting of a real Hilbert space. We then prove that a sequence generated by the algorithm converges strongly to such common element which also approximates solution of some fixed point problem of demimetric mapping in the space. Finally, some applications and numerical experiment are given to show effectiveness of the proposed algorithm over the recently known related results in the literature. The established results extend and generalize many recent ones announced in the literature.

show abstract

“…lim n→∞ c n /γ n = 0. Also, from (10), θ n ≤ θn ≤ c n / x n − x n−1 for all n ≥ 1 and x n = x n−1 . This implies…”

Section: Algorithmmentioning

confidence: 99%

Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces

Ugwunnadi

Haruna

Harbau

2023

Carpathian Math. Publ.

View full text Add to dashboard Cite

show abstract

“…Furthermore, the general system of variational inequalities problem has been studied and developed in many literatures, see previous studies. ()…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the general system of variational inequalities problem has been studied and developed in many literatures, see previous studies. [12][13][14][15][16][17][18][19][20][21] Let H 1 , H 2 be two real Hilbert spaces. Let C, Q be nonempty closed convex subsets of H 1 and H 2 , respectively.…”

mentioning

confidence: 99%

Algorithm method for solving the split general system of variational inequalities problem and fixed point problem of nonexpansive mapping with application

Siriyan

Kangtunyakarn

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

The purpose of this research is to introduce the split general system of variational inequalities problem, by using the concept of the general system of variational inequalities problem in Ceng et al. Then, we establish and prove a strong convergence theorem for finding a common element of the set of solutions of this problem and the set of fixed points of a nonexpansive mapping for the first time in this research. By using our main theorem, strong convergence theorems of the split feasibility problem, the split variational inequality problem, and the minimization problem are obtained, respectively. In order to show the potential of our main result, we give three numerical examples of these classical problems introduced by previous studies, with the numerical example of our main theorem to compare the rate of convergence.

show abstract

“…The general system of variational inclusions (GSVI) is to find (x * , y * ) ∈ C × C such that 0 ∈ x * − y * + ρ 1 (A 1 y * + M 1 x * ), 0 ∈ y * − x * + ρ 2 (A 2 x * + M 2 y * ), (4) where ρ 1 and ρ 2 are two positive constants. In 2010, Qin et al [4] introduced a relaxed extragradient-type method for solving GSVI (4), and proved a strong convergence theorem for the proposed method (for its related results in the literature, see, e.g., [1,[5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Furthermore, Aoyama et al [19] considered the following variational inequality: Find…”

Section: Introductionmentioning

confidence: 99%

“…where η > 0 is a constant and Π C is a sunny nonexpansive retraction from E onto C. In particular, if E = H a Hilbert space, then Π C coincides with the metric projection P C from H onto C. Recently, many authors have studied the problem of finding a common element of the set of fixed points of nonlinear mappings and the set of solutions to variational inequalities by iterative methods (see, e.g., [1][2][3]5,6,[8][9][10]12,[14][15][16][18][19][20][21][22][23][24]).…”

Section: Introductionmentioning

confidence: 99%

System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

et al. 2018

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to solve the general system of variational inclusions (GSVI) with hierarchical variational inequality (HVI) constraint, for an infinite family of continuous pseudocontractive mappings in Banach spaces. By utilizing the equivalence between the GSVI and the fixed point problem, we construct an implicit multiple-viscosity approximation method for solving the GSVI. Under very mild conditions, we prove the strong convergence of the proposed method to a solution of the GSVI with the HVI constraint, for infinitely many pseudocontractions.Keywords: implicit multiple viscosity approximation method; system of variational inclusions; pseudocontractive mapping; nonexpansive mapping MSC: 47H05; 47H10; 47J25

show abstract

Systems of variational inequalities with hierarchical variational inequality constraints in Banach spaces

Cited by 6 publications

References 21 publications

Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces

Accelerated Krasnoselski-Mann type algorithm for hierarchical fixed point and split monotone variational inclusion problems in Hilbert spaces

Algorithm method for solving the split general system of variational inequalities problem and fixed point problem of nonexpansive mapping with application

System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces

Contact Info

Product

Resources

About