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A first-order semilinear fuzzy differential inclusion with fuzzy impulse characteristics and linear boundary conditions is considered in separable Banach spaces. By means of semigroup properties, stacking approach and the fixed point theorem for multivalued map due to Dhage, the existence results for fuzzy solution are established. Some general criteria are presented for a class of semilinear fuzzy differential inclusions including higher dimensional and infinite dimensional uncertain systems, and the conditions for existence of solutions in the results are concise and mild. Also, several examples are given to illustrate the utility and applicability. [ABSTRACT FROM AUTHOR]

Abstract: A second order semilinear differential inclusion with some boundary continuous and impulse characteristics in a separable Banach space is considered. Some existence theorems for mild solutions are given, when the multivalued nonlinearity of the inclusion is only a locally integrably bounded upper-Carathéodory map with convex and weakly compact values. Then the compactness of the set of all mild solutions for the problem is proved. The results are obtained by using the theory of continuous cosine families of bounded linear operators and a fixed point theorem for multivalued maps due to Agarwal, Meehan and O’Regan. A corresponding result for closed graph of composition is extended. [Copyright &y& Elsevier]

Abstract: The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and the existence of Chebyshev solutions for an integral inclusion is proved. [Copyright &y& Elsevier]

Abstract: A new continuity theorem of minimum selection is presented for a continuous set-valued operator from a topological space into a Banach space with some uniform convexity. As applications, some problems concerning minimum right inverses for linear operators and minimum fixed points for condensing set-valued nonlinear operators are discussed. Also, the existence of minimum solutions for an integral inclusion is proved. [Copyright &y& Elsevier]

Abstract: In this paper a -step iterative scheme with error terms involving asymptotically quasi-nonexpansive mappings is studied. In usual Banach spaces, some sufficient and necessary conditions are given for the iterative scheme to approximate a common fixed point. In uniformly convex Banach spaces, power equicontinuity for a mapping is introduced and a series of new convergence theorems are established. Several known results in the current literature are extended and refined. [Copyright &y& Elsevier]

In this paper a modified Ishikawa iterative process for approximating a common fixed point of a locally asymptotically nonexpansive cosine family is firstly introduced, and then, by using the theory of cosine families and constructing some control conditions, several strong convergence theorems are established for this iterative process in Banach spaces. Moreover, an example is presented to illustrate the main result of the paper. [ABSTRACT FROM AUTHOR]