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Iterative solution of nonlinear equations of the pseudo-monotone type in Banach spaces

A. M. Saddeek, Sayed A. Ahmed (2008)

Archivum Mathematicum

The weak convergence of the iterative generated by J ( u n + 1 - u n ) = τ ( F u n - J u n ) , n 0 , ( 0 < τ = min { 1 , 1 λ } ) to a coincidence point of the mappings F , J : V V is investigated, where V is a real reflexive Banach space and V its dual (assuming that V is strictly convex). The basic assumptions are that J is the duality mapping, J - F is demiclosed at 0 , coercive, potential and bounded and that there exists a non-negative real valued function r ( u , η ) such that sup u , η V { r ( u , η ) } = λ < ...

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