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Perturbed Hammerstein integral inclusions with solutions that change sign

Gennaro Infante, Paolamaria Pietramala (2009)

Commentationes Mathematicae Universitatis Carolinae

We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of [ 0 , 1 ] . We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.

Perturbed Proximal Point Algorithm with Nonquadratic Kernel

Brohe, M., Tossings, P. (2000)

Serdica Mathematical Journal

Let H be a real Hilbert space and T be a maximal monotone operator on H. A well-known algorithm, developed by R. T. Rockafellar [16], for solving the problem (P) ”To find x ∈ H such that 0 ∈ T x” is the proximal point algorithm. Several generalizations have been considered by several authors: introduction of a perturbation, introduction of a variable metric in the perturbed algorithm, introduction of a pseudo-metric in place of the classical regularization, . . . We summarize some of these extensions...

Preface

Zbigniew Bartosiewicz, Ewa Girejko (2006)

Control and Cybernetics

Properties of generalized set-valued stochastic integrals

Michał Kisielewicz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...

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