Abstract
In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings.MSC:47H09, 47H10, 47L25.
Highlights
Let E be a real Banach space with dual E∗
It is well known that E is smooth if and only if J is single-valued and if E is uniformly smooth J is uniformly continuous on bounded subsets of E
4 Applications we study the problem of finding a minimizer of a continuously Fréchet differentiable convex functional in Banach spaces
Summary
Let E be a real Banach space with dual E∗. A normalized duality mapping J : E → E∗ is defined byJx = f ∗ ∈ E∗ : x, f ∗ = x = f ∗ , where ·, · denotes the generalized duality pairing between E and E∗.
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