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Let E be a reflexive Banach space with a uniformly GÃƒÂ¢teaux differentiable norm, let K be a nonempty closed convex subset of E, and let T:KÃ¢Â†Â’K be a uniformly continuous pseudocontraction. If f:KÃ¢Â†Â’K is any contraction map on K and if every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers {ÃŽÂ±n}, {ÃŽÂ¼n}, that the iteration process z1Ã¢ÂˆÂˆK, zn+1=ÃŽÂ¼n(ÃŽÂ±nTzn+(1Ã¢ÂˆÂ’ÃŽÂ±n)zn)+(1Ã¢ÂˆÂ’ÃŽÂ¼n)f(zn), nÃ¢ÂˆÂˆÃ¢Â„Â•, strongly converges to the fixed point of T, which is the unique solution of some variational inequality, provided that K is bounded

Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces