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Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes

Biagio Ricceri (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this Note we first establish a result on the structure of the set of fixed points of a multi-valued contraction with convex values. As a consequence of this result, we then obtain the following theorem: Let ( U , U ) , ( V , V ) be two real Banach spaces and let Φ be a continuous linear operator from U onto V . Put: α = sup { inf { u U : u Φ - 1 ( v ) } : v V , v V 1 } . Then, for every v V and every lipschitzian operator Ψ : U V , with Lipschitz constant L such that α L < 1 , the set { u U : Φ ( u ) + Ψ ( u ) = v } is non-empty and arc wise connected.

Upper and lower solutions method for partial Hadamard fractional integral equations and inclusions

Saïd Abbas, Eman Alaidarous, Wafaa Albarakati, Mouffak Benchohra (2015)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we use the upper and lower solutions method combined with Schauder's fixed point theorem and a fixed point theorem for condensing multivalued maps due to Martelli to investigate the existence of solutions for some classes of partial Hadamard fractional integral equations and inclusions.

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