A STRONG CONVERGENCE THEOREM FOR ZEROS OF BOUNDED MAXIMAL MONOTONE MAPPINGS IN BANACH SPACES WITH APPLICATIONS

Author (s) : S.Lavanya ,A.Kavitha & V.Nandhini

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Abstract :
let e be a uniformly convex and uniformly smooth real banach space and e be its dual. let a : e ! 2e be a bounded maximal monotone map. assume that a?1(0) 6= ;. a new iterative sequence is constructed which converges strongly to an element of a?1(0). the theorem proved, complements results obtained on strong convergence of the proximal point algorithm for approximating an element of a?1(0) (assuming existence) and also resolves an important open question. furthermore, this result is applied to convex optimization problems and to variational inequality problems. these results are achieved by combining a theorem of riech on the strong convergence of the resolvent of maximal monotone mappings in a uniformly smooth real banach space; new geometric properties of uniformly convex and uniformly smooth real banach spaces introduced by alber with a technique of proof which is also of independent interest.

Keywords : Convergence Theorem, Monotone mapping

Conference Date : 30/08/2019

Pages : 342

Paper ID : 19333