/pdf/fixed-points-of-nonexpansive-type-multivalued-maps-2uhaukv0hw.pdf

Fixed points of nonexpansive type multivalued maps

We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an -inverse strongly monotone mapping and a fixed point of relatively non-expansive mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-linear operators.

Minimum-norm solution of variational inequality and fixed point problem in banach spaces

We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings T in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path z t ∈ t u + ( 1 − t ) T z t .

Convergence of iterative algorithms for multivalued mappings in Banach spaces

We first investigate strong convergence of the sequence generated by implicit and explicit viscosity approximation methods for a one-parameter nonexpansive semigroup in a real Banach space E which has a uniformly Gâteaux differentiable norm and admits the duality mapping j ? , where ? is a gauge function on [0, ?). The main results also improve and extend some known results concerning the normalized duality mapping in the literature.

Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions

We study in this paper the existence and the approximation of solutions of variational inequalities involving generalized pseudocontractive mappings in Banach spaces. The convergence analysis of a proposed hybrid iterative method for approximating common zeros or fixed points of a possibly infinitely countable or uncountable family of such operators will be conducted within the conceptual framework of the “viscosity approximation technique” in reflexive Banach spaces with uniform Gâteaux differentiable norms. This technique should make existing or new results in solving variational inequalities more applicable.

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Sumei Xu

Papers

Strong convergence theorems for nonexpansive semigroup in Banach spaces