ITERATIVE SOLUTION OF NONLINEAR EQUATIONS OF THE PSEUDO-MONOTONE TYPE IN BANACH SPACES
Sayed A. Ahmed · Archivum Mathematicum · 2008
The weak convergence of the iterative generated by J(un+1 un) = (Fun Jun), n 0, 0 < = min 1, 1 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, ) such that sup u, 2V {r(u, )} = < 1 r(u, )kJ(u )kV ?k (J F)(u) (J F)( )kV ? , 8 u, 2 V. Furthermore, the case when V is a Hilbert space is given. An application of our results to filtration problems with limit gradient in a domain with semipermeable boundary is also provided.