Iterative Algorithms for Finding Approximate Solutions for General Strongly Nonlinear Variational Inequalities

Liu, Zeng

doi:10.1006/jmaa.1994.1361

Cited by 45 publications

(16 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…6. Theorem 3.1 of Chang [4], generalizes and improves the results in [16,17,18,21,27,28,30], so Theorems 3.1 and 3.3 extend and establish random generalization of the work of [16,17,18,21,27,28,30].…”

Section: Applicationsmentioning

confidence: 78%

Some Strong Convergence Results of Random Iterative Algorithms With Errors in Banach Spaces

Chugh¹,

Kumar²,

Narwal³

2016

Communications of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.

show abstract

Section: Applicationsmentioning

confidence: 78%

Some Strong Convergence Results of Random Iterative Algorithms With Errors in Banach Spaces

Chugh¹,

Kumar²,

Narwal³

2016

Communications of the Korean Mathematical Society

View full text Add to dashboard Cite

show abstract

“…(III) If for all x, y ∈ K, η(y, x) = y − x, and f (x) = 0, then problem (1) reduces to the strongly nonlinear variational inequality problem considered by Siddiqi and Ansari [10] , and Zeng [12,13] : find x * ∈ K such that…”

Section: Some Special Cases (I) Ifmentioning

confidence: 99%

Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities

Zeng

2004

Acta Mathematicae Applicatae Sinica, English Series

View full text Add to dashboard Cite

The purpose of this paper is to investigate the iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities in a real Hilbert space, where the iterative algorithm is presented by virtue of the auxiliary principle technique. On one hand, the existence of approximate solutions of this class of mixed variational-like inequalities is proven. On the other hand, it is shown that the approximate solutions converge strongly to the exact solution of this class of mixed variational-like inequalities.

show abstract

“…In the setting of Hilbert spaces, one of the most efficient numerical techniques is the projection method and its variant forms; see 4,[6][7][8][9][10][11][12][13][14][15] . Since the standard projection method strictly depends on the inner product property of Hilbert spaces, it can no longer be applied for general mixed type variational inequalities in Banach spaces.…”

Section: Fixed Point Theory and Applicationsmentioning

confidence: 99%

Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space

Ceng

Kum

Yao

2010

Fixed Point Theory Appl

View full text Add to dashboard Cite

Let B be a real Banach space with the dual space B * . Let φ : B → R ∪ { ∞} be a proper functional and let Θ : B × B → R be a bifunction. In this paper, a new concept of η-proximal mapping of φ with respect to Θ is introduced. The existence and Lipschitz continuity of the η-proximal mapping of φ with respect to Θ are proved. By using properties of the η-proximal mapping of φ with respect to Θ, a generalized mixed equilibrium problem with perturbation for short, GMEPP is introduced and studied in Banach space B. An existence theorem of solutions of the GMEPP is established and a new iterative algorithm for computing approximate solutions of the GMEPP is suggested. The strong convergence criteria of the iterative sequence generated by the new algorithm are established in a uniformly smooth Banach space B, and the weak convergence criteria of the iterative sequence generated by this new algorithm are also derived in B H a Hilbert space.

show abstract

Iterative Algorithms for Finding Approximate Solutions for General Strongly Nonlinear Variational Inequalities

Cited by 45 publications

References 0 publications

Some Strong Convergence Results of Random Iterative Algorithms With Errors in Banach Spaces

Some Strong Convergence Results of Random Iterative Algorithms With Errors in Banach Spaces

Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities

Algorithm for Solving a Generalized Mixed Equilibrium Problem with Perturbation in a Banach Space

Contact Info

Product

Resources

About