✦ LIBER ✦

Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space

✍ Scribed by Satoru Takahashi; Wataru Takahashi

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 228 KB
Volume: 69
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.02.042

No coin nor oath required. For personal study only.

✦ Synopsis

We introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain that the sequence converges strongly to a common element of two sets. Using this result, we prove three new strong convergence theorems in fixed point problems, variational inequalities and equilibrium problems.

📜 SIMILAR VOLUMES

Strong and weak convergence theorems for

Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces

✍ Wataru Takahashi; Kei Zembayashi 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 579 KB

Strong convergence theorems for relative

Strong convergence theorems for relatively nonexpansive mappings in a Banach space

✍ Xiaolong Qin; Yongfu Su 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 210 KB

Convergence of a general iterative metho

Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces

✍ Yeol Je Cho; Xiaolong Qin 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 481 KB

In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding res

Strong convergence theorems of hybrid me

Strong convergence theorems of hybrid methods for two asymptotically nonexpansive mappings in Hilbert spaces

✍ Issara Inchan; Somyot Plubtieng 📂 Article 📅 2008 🏛 Elsevier 🌐 English ⚖ 659 KB

Strong convergence theorem for a family

Strong convergence theorem for a family of Lipschitz pseudocontractive mappings in a Hilbert space

✍ Qing-bang Zhang; Cao-zong Cheng 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 190 KB

Weak and strong convergence theorems for

Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces

✍ Yu Kurokawa; Wataru Takahashi 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 259 KB

In this paper, we first obtain a weak mean convergence theorem of Baillon's type for nonspreading mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem for nonspreading mappings in a Hilbert space.