Abstract
In this study, Mann-type iterative process is considered for finding a common element in the fixed point set of strict pseudocontractions and in the zero point set of the operator which is the sum of inverse strongly- monotone operators and maximal monotone operators. Weak convergence theorems of common elements are established in the framework of Hilbert spaces. Some applications of main results are also provided. AMS Subject Classification: 47H05; 47H09; 47J25; 90C33.
Highlights
1 Introduction and preliminaries Throughout this article, we always assume that H is a real Hilbert space with the inner product 〈 ·, ·〉, and the norm ||·|| and that C is a nonempty closed convex subset of H
Marino and Xu [17] proved that fixed point sets of strictly pseudocontractive mappings are closed and convex
The results presented in this article improve and extend the corresponding results announced by Tada and Takahashi [11] and Takahshi and Toyoda [13]
Summary
Introduction and preliminariesThroughout this article, we always assume that H is a real Hilbert space with the inner product 〈 ·, ·〉, and the norm ||·|| and that C is a nonempty closed convex subset of H.Let A : C ® H be a mapping. Marino and Xu [17] proved that fixed point sets of strictly pseudocontractive mappings are closed and convex.
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