Fixed Point Theory of Multivalued Weighted Maps

Pejsachowicz, Jacobo; Skiba, Robert

doi:10.1007/1-4020-3222-6_6

Cited by 6 publications

(3 citation statements)

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“…Furthermore, the results presented in this section remain valid for multivalued weighted maps. For more details about multivalued weighted maps we recommend: [22,24,25], and the references therein.…”

Section: Definition 52 (Seementioning

confidence: 99%

On a generalization of absolute neighborhood retracts

Skiba

Ślosarski

2009

Topology and its Applications

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Section: Definition 52 (Seementioning

confidence: 99%

On a generalization of absolute neighborhood retracts

Skiba

Ślosarski

2009

Topology and its Applications

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“…The topological fixed point theory for multivalued maps has been developed in two main directions: (i) for admissible maps (in the sense of Górniewicz) and their particular cases like acyclic maps, R δ -maps, and so forth (see e.g., References [22,25,26], and the references therein), and (ii) for n-valued maps (see e.g., References [20][21][22][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]) and their generalizations like n-acyclic maps (see e.g., Reference [49]) and weighted maps (see e.g., Reference [50]). In the present paper, we will be exclusively interested in the second class of n-valued maps whose research made a big progress in the recent years.…”

Section: N-valued Mapsmentioning

confidence: 99%

Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n-Valued Impulses

Andres

2020

Mathematics

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Ordinary differential equations with n-valued impulses are examined via the associated Poincaré translation operators from three perspectives: (i) the lower estimate of the number of periodic solutions on the compact subsets of Euclidean spaces and, in particular, on tori; (ii) weakly locally stable (i.e., non-ejective in the sense of Browder) invariant sets; (iii) fractal attractors determined implicitly by the generating vector fields, jointly with Devaney’s chaos on these attractors of the related shift dynamical systems. For (i), the multiplicity criteria can be effectively expressed in terms of the Nielsen numbers of the impulsive maps. For (ii) and (iii), the invariant sets and attractors can be obtained as the fixed points of topologically conjugated operators to induced impulsive maps in the hyperspaces of the compact subsets of the original basic spaces, endowed with the Hausdorff metric. Five illustrative examples of the main theorems are supplied about multiple periodic solutions (Examples –) and fractal attractors (Examples and ).

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“…( [25], [26]), many known Lefschetz fixed point theorems (e.g. [3], [10], [17], [24], [26], [27], [29], [30], [33], [34], [37]- [40]) follow from Theorem 4 in Section 5.5.…”

Section: Introductionmentioning

confidence: 99%