Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces
نویسندگان
چکیده
منابع مشابه
Strong Convergence Theorems for Generalized Variational Inequalities and Relatively Weak Nonexpansive Mappings in Banach Spaces
In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational ...
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متن کاملWeak and strong convergence theorems for relatively nonexpansive multi-valued mappings in Banach spaces
* Correspondence: [email protected] Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34149-16818, Qazvin, Iran Full list of author information is available at the end of the article Abstract In this paper, an iterative sequence for relatively nonexpansive multi-valued mappings by using the notion of generalized projection is introduced, and th...
متن کاملWeak and Strong Convergence Theorems for Relatively Nonexpansive Mappings in Banach Spaces
where {rn} ⊂ (0,∞) and Jr = (I + rA)−1 for all r > 0. This algorithm was first introduced by Martinet [9]. In [16], Rockafellar proved that if liminfn→∞ rn > 0 and A−10 = ∅, then the sequence {xn} defined by (1.2) converges weakly to an element of solutions of (1.1). On the other hand, Kamimura and Takahashi [4] considered an algorithm to generate a strong convergent sequence in a Hilbert space...
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and Applied Analysis 3 Remark 1.6. The examples of weak relatively uniformly nonexpansive multivalued mapping can be found in Su 1 and Homaeipour and Razani 2 . Let E be a real Banach space, and let E∗ be the dual space of E. Let f be a bifunction from C × C to R. The equilibrium problem is to find x̂ ∈ C such that fx̂, y ≥ 0, ∀y ∈ C. 1.3 The set of solutions of 1.3 is denoted by EP f . Given a m...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2004
ISSN: 1687-1812
DOI: 10.1155/s1687182004310089