Decomposability and uniform integrability in Pettis integration

In this paper, we give several characterizations of decomposable subsets of the space of Pettis integrable functions (in particular, a characterization similar to that already known in the Bochner integrability setting). We also introduce the notion WPUI of uniform integrability, and obtain some relations between decomposability and PUI, resp. WPUI uniform integrability concepts. As consequence, conditional weak compactness and sequential weak compactness criteria are given under decomposability assumptions. Finally, an application to second order differential inclusions is presented. Keywords: Pettis integral, decomposability, set-valued integral, uniform integrability, sequential weak compactness, differential inclusionQuaestiones Mathematicae 29(2006), 39–5

COMMON FIXED POINT THEOREMS FOR PAIRS OF SUBCOMPATIBLE MAPS

In this paper, we introduce the new concepts of subcompatibility and subsequential continuity which are respectively weaker than occasionally weak compatibility and reciprocal continuity. With them, we establish a common fixed point theorem for four maps in a metric space which improves a recent result of Jungck and Rhoades [7]. Also we give another common fixed point theorem for two pairs of subcompatible maps of Greguˇs type which extends results of the same authors, Djoudi and Nisse [3], Pathak et al. [12] and others and we end our work by giving a third result which generalizes results of Mbarki [8] and others. Key words and phrases: Commuting and weakly commuting maps, compatible and compatible maps of type (A), (B), (C) and (P), weakly compatible maps, occasionally weakly compatible maps, subcompatible maps, subsequentially continuous maps, coincidence point, common fixed point, Greguˇs type

Young Measures and Compactness in Measure Spaces

Many problems in science can be formulated in the language of optimization theory, in which case an optimal solution or the best response to a particular situation is required. In situations of interest, such classical optimal solutions are lacking, or at least, the existence of such solutions is far from easy to prove. So, non-convex optimization problems may not possess a classical solution because approximate solutions typically show rapid oscillations. This phenomenon requires the extension of such problems' solution often constructed by means of Young measures. This book is written to in

On Fractional Evolution Inclusion Coupled with a Time and State Dependent Maximal Monotone Operator

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On Fractional Differential Inclusions with Nonlocal Boundary Conditions

International audienc