Name
Title | ||
|---|---|---|
Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions |
Abstract | ||
|---|---|---|
In the present paper, we introduce the concept of @h-relaxed strong convexity of a differentiable functional and extend Ding and Yao's auxiliary variational inequality technique [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Computers and Mathematics with Applications, 49 (2005), 857-869] to develop iterative algorithms for finding the approximate solutions to the mixed quasi-variational-like inclusion problem (in short, MQVLIP) in a Banach space. On the one hand, we establish a result on the existence of a solution to the equilibrium problem by virtue of well-known Brouwer's fixed-point theorem. Moreover, by using this result we derive the existence and uniqueness of a solution to the MQVLIP and the existence of the approximate solutions generated by the algorithm for the MQVLIP. On the other hand, we use the concepts of @h-relaxed strong convexity of a differentiable functional and @h-cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the MQVLIP. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2008.01.024 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
h-relaxed strong convexity,unique solution,j.c. yao,mixed quasi-variational-like inclusion,iterative algorithm,strong convergence,p. ding,approximate solution,banach space,equilibrium problem,brouwer’s fixed-point theorem,auxiliary variational inequality,fixed point theorem,variational inequality | Convergence (routing),Uniqueness,Picard–Lindelöf theorem,Mathematical optimization,Convexity,Mathematical analysis,Iterative method,Banach space,Differentiable function,Mathematics,Variational inequality | Journal |
Volume | Issue | ISSN |
56 | 4 | Computers and Mathematics with Applications |
Citations | PageRank | References |
3 | 0.49 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lu-Chuan Ceng | 1 | 134 | 23.86 |
| Sy-Ming Guu | 2 | 493 | 37.65 |
| Jen-chih Yao | 3 | 504 | 100.09 |