In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. ...

Enlargements have proven to be useful tools for studying maximally monotone mappings. It is therefore natural to ask in which cases the enlargement does not change the original mapping. Svaiter has recently characterized non-enlargeable operators in reflexive Banach spaces and has also given some partial results in the nonreflexive case. In the present paper, we provide another characterization...

Let X be either a uniformly convex Banach space or a reflexive Banach space having the Opial property. It is shown that a multivalued nonexpansive mapping on a bounded closed convex subset of X has an endpoint if and only if it has the approximate endpoint property. This is the first result regarding the existence of endpoints for such kind of mappings even in Hilbert spaces. The related result...

By making use of duality mappings and the Bregman distance, we propose a regularizing Levenberg-Marquardt scheme to solve nonlinear inverse problems in Banach spaces, which is an extension of the one proposed in [6] in Hilbert space setting. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme involves a family of convex minimization problems in...

We introduce and study a new class of general nonlinear random multivalued operator equations involving generalized m-accretive mappings in Banach spaces. By using the Chang’s lemma and the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang 2001 , we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative...

The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gâteaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key elem...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of themappings. Next, using this operator, we construct an iterative sequence to approximate common fixed point...

We introduce an iterative scheme for finding a common element of the set of solutions of generalizedmixed equilibrium problems and the set of fixed points for countable families of total quasi-φasymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly co...

The inequality Ffx;fy(qs) Fx;y(s) (s 0), where q 2 (0; 1), is generalized for multivalued mappings in many directions. Using Hausdor distance S.B. Nadler in [7] introduced a generalization of Banach contraction principle in metric spaces. In [3] the de nition of probabilistic Nadler q-contraction is given. Using some results given in [12] a xed point theorem on spaces with a convex structure is...