New semi-implicit midpoint rule for zero of monotone mappings in Banach spaces

Abstract

Let E be a nonempty closed uniformly convex and 2-uniformly smooth Banach space with dual E * and A : E * → E be Lipschitz continuous monotone mapping with A −1 (0) = ∅. A new semi-implicit midpoint rule (SIMR) with the general contraction for monotone mappings in Banach spaces is established and proved to converge strongly to x * ∈ E, where J x * ∈ A −1 (0). Moreover, applications to convex minimization problems, solution of Hammerstein integral equations, and semi-fixed point of a cluster of semi-pseudo mappings are included.

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