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Recently, two retractions (projections), which are different from the metric projection and the sunny nonexpansive retraction in a Banach space, were found. In this article, using nonlinear analytic methods and new retractions, we prove a nonlinear ergodic theorem for positively homogeneous and nonexpansive mappings in a uniformly convex Banach space. The limit points are characterized by using new retractions. [ABSTRACT FROM PUBLISHER]

Our aim is to study fractional order differential inclusions with infinite delays in Banach spaces. We impose the regularity condition on multivalued nonlinearity in terms of measures of noncompactness to get the existence result. Some properties of the solution map are proved. [ABSTRACT FROM PUBLISHER]

We study the abstract Cauchy problem for a class of integrodifferential equations in a Banach space with nonlinear perturbations and nonlocal conditions. By using MNC estimates, the existence and continuous dependence results are proved. Under some additional assumptions, we study the topological structure of the solution set. [ABSTRACT FROM AUTHOR]

Abstract: Let be a real Banach space with a uniformly Gâteaux differentiable norm and which possesses uniform normal structure, a nonempty bounded closed convex subset of , a finite family of asymptotically nonexpansive self-mappings on with common sequence , be two sequences in (0, 1) such that and be a contraction on . Under suitable conditions on the sequences , we show the existence of a sequence satisfying the relation where for some unique integers and . Further we prove that converges strongly to a common fixed point of , which solves some variational inequality, provided as for . As an application, we prove that the iterative process defined by , converges strongly to the same common fixed point of . [Copyright &y& Elsevier]

In this paper, we introduce a new class of generalized co-complementarity problems in Banach spaces. An iterative algorithm for finding approximate solutions of these problems is considered. Some convergence results for this iterative algorithm are derived and several existence results are obtained. [Copyright &y& Elsevier]

The Opial property of Hilbert spaces is essential in many fixed point theorems of non-expansive maps. While the Opial property does not hold in every Banach space, the Bregman–Opial property does. This suggests to study fixed point theorems for various Bregman non-expansive like maps in the general Banach space setting. In this paper, after introducing the notion of Bregman generalized hybrid sequences in a reflexive Banach space, we prove (with using the Bregman–Opial property instead of the Opial property) convergence theorems for such sequences. We also provide new fixed point theorems for Bregman generalized hybrid maps defined on an arbitrary but not necessarily convex subset of a reflexive Banach space. We end this paper with a brief discussion of the existence of Bregman absolute fixed points of such maps. [ABSTRACT FROM AUTHOR]

Let P w ( E n ; F ) be the space of all continuous n -homogeneous polynomials from a Banach space E into another F , that are weakly continuous on bounded sets. We give sufficient conditions for the weak sequential completeness of P w ( E n ; F ) . These sufficient conditions are also necessary if both E ⁎ and F have the bounded compact approximation property. We also show that the weak sequential completeness and the reflexivity of P w ( E n ; F ) are equivalent whenever both E and F are reflexive. [ABSTRACT FROM AUTHOR]

Abstract: Let be standard operator algebras on complex Banach spaces , respectively. For , let be a sequence with terms chosen from , and define the generalized Jordan product on elements in . This includes the usual Jordan product , and the triple . Assume that at least one of the terms in appears exactly once. Let a map satisfy that whenever any one of has rank at most one. It is shown in this paper that if the range of contains all operators of rank at most three, then must be a Jordan isomorphism multiplied by an th root of unity. Similar results for maps between self-adjoint operators acting on Hilbert spaces are also obtained. [Copyright &y& Elsevier]

Abstract: Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. In his classic paper published in 1983, Browder developed a degree theory for mappings of monotone type , where f is a mapping of class from a bounded open set Ω in a reflexive Banach space X into its dual , and T is a maximal monotone mapping from X into . This breakthrough paved the way for many applications of degree theoretic techniques to several large classes of nonlinear partial differential equations. In this paper we continue to develop the results of Browder on the degree theory for mappings of monotone type . By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. [Copyright &y& Elsevier]