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Displaying similar documents to “A generalization of the Schauder fixed point theorem via multivalued contractions”

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with p -decomposable values

Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)

Studia Mathematica

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We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex L p ( T , E ) -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, L p ( T , E ) is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...

Implicit integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1997)

Commentationes Mathematicae Universitatis Carolinae

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We consider the integral equation h ( u ( t ) ) = f ( ∫ I g ( t , x ) u ( x ) d x ) , with t ∈ [ 0 , 1 ] , and prove an existence theorem for bounded solutions where f is not assumed to be continuous.

On convex and *-concave multifunctions

Bożena Piątek (2005)

Annales Polonici Mathematici

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A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion 1 / ( t - s ) ∫ s t F ( x ) d x ⊂ ( F ( s ) * + F ( t ) ) / 2 holds for every s,t ∈ [a,b], s < t.

Semicontinuity and continuous selections for the multivalued superposition operator without assuming growth-type conditions

Hông Thái Nguyêñ (2004)

Studia Mathematica

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Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction f : Ω × E → 2 F , denote by N f ( x ) the set of all measurable selections of the multifunction f ( · , x ( · ) ) : Ω → 2 F , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator N f mapping some open domain G ⊂ X into 2 Y , where X and Y are...

Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: i n f y ∈ Y s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X i n f y ∈ Y g ( x , y ) . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: s u p x ∈ X f ( x , y ) ≤ s u p x ∈ X g ( x , y ) , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some...

Multivalued pseudo-contractive mappings defined on unbounded sets in Banach spaces

Claudio H. Morales (1992)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a real Banach space. A multivalued operator T from K into 2 X is said to be pseudo-contractive if for every x , y in K , u ∈ T ( x ) , v ∈ T ( y ) and all r > 0 , ∥ x - y ∥ ≤ ∥ ( 1 + r ) ( x - y ) - r ( u - v ) ∥ . Denote by G ( z , w ) the set { u ∈ K : ∥ u - w ∥ ≤ ∥ u - z ∥ } . Suppose every bounded closed and convex subset of X has the fixed point property with respect to nonexpansive selfmappings. Now if T is a Lipschitzian and pseudo-contractive mapping from K into the family of closed and bounded subsets of K so that the set G ( z , w ) is bounded for some z ∈ K and some w ∈ T ( z ) , then T has a fixed point in K . ...