𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Iterative process with errors for fixed points of multivalued Φ-hemicontractive operators in uniformly smooth Banach spaces

✍ Scribed by Zhenyu Huang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
508 KB
Volume
39
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

This paper proves that, under suitable conditions, the multivalued Ishikawa iterative sequence with errors strongly converges to the unique fixed point of T. The related result deals with the strong convergence of the Ishikawa iterative sequence with errors to the unique solution of the equation f E Tx when T : E --* 2 E is multivalued C-strongly accretive. These results generalize the results of the author [1], Ding [2,3], Osilike [4,5], Zhou [6,7], and Chidume [8,9] into more general multivalued ¢-hemicontractive operators without the continuous assumption on operators T.

📜 SIMILAR VOLUMES

Approximations for fixed points of φ-hem
Approximations for fixed points of φ-hemicontractive mappings by the Ishikawa iterative process with mixed errors
✍ Yeol Je Cho; Haiyun Zhou; Shin Min Kang; Seong Sik Kim 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 650 KB

X be a real uniformly smooth Banach space, K be a nonempty closed convex subset of X and T K + K be a generalized Lrpschrtzran and hemrcontractrve mapping It IS shown that the Ishlkawa iterative process with mrxed errors converges strongly to the unique fixed pomt of the mapping T As consequences, s

Iterative solutions of nonlinear equatio
Iterative solutions of nonlinear equations with φ-strongly accretive operators in uniformly smooth Banach spaces
✍ Zeqing Liu; S.M. Kang 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 814 KB

Suppose that X is a uniformly smooth Banach space and T : X -X is a demicontinuous (not necessarily Lipschitz) #-strongly accretive operator. It is proved that the Ishikawa iterative method with errors converges strongly to the solutions of the equations f = TX and f = z+Tx, respectively. A related

Approximating the fixed points of φ-hemi
Approximating the fixed points of φ-hemicontractions by the Ishikawa iterative process with mixed errors in normed linear spaces
✍ Haiyun Zhou; Y.J. Cho; Shih-sen Chang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 307 KB

Let \(X\) be a real normed linear space, \(K\) be a nonempty and convex subset of \(X\) and \(T: K \rightarrow K\) be a uniformly continuous and hemicontractive mapping. It is shown that the Ishikawa iterative process with mixed errors converges strongly to the unique fixed point of \(T\). As conseq

The p-step iterative algorithm for a sys
The p-step iterative algorithm for a system of generalized mixed quasi-variational inclusions with -accretive operators in q-uniformly smooth banach spaces
✍ Xie Ping Ding; Hai Rong Feng 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 216 KB

In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (A, )-accretive operators in q-uniformly smooth Banach spaces. By using the resolvent operator technique associated with (A, )-accretive operators, we construct a new p-step iterative algorithm