Displaying similar documents to “Fixed points for generalized multi-valued contractions”

Fixed point theorems for set-valued Y-contractions

Ioan A. Rus, Adrian Petruşel, Gabriela Petruşel (2007)

Banach Center Publications

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The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.

Fixed Points of n-Valued Multimaps of the Circle

Robert F. Brown (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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A multifunction ϕ: X ⊸ Y is n-valued if ϕ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps ϕ: S¹ ⊸ S¹ are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(ϕ) of an n-valued ϕ: S¹ ⊸ S¹ of degree d equals |n - d| and ϕ is homotopic to an n-valued power map that has exactly |n - d| fixed points. Thus the Wecken property, that Schirmer established...

Fixed point and continuation results for contractions in metric and gauge spaces

M. Frigon (2007)

Banach Center Publications

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We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.

Note on the selection properties of set-valued semimartingales

Mariusz Michta (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

Set-valued Stratonovich integral

Anna Góralczyk, Jerzy Motyl (2006)

Discussiones Mathematicae Probability and Statistics

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The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

Cauchy Mean Theorem

Adam Grabowski (2014)

Formalized Mathematics

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The purpose of this paper was to prove formally, using the Mizar language, Arithmetic Mean/Geometric Mean theorem known maybe better under the name of AM-GM inequality or Cauchy mean theorem. It states that the arithmetic mean of a list of a non-negative real numbers is greater than or equal to the geometric mean of the same list. The formalization was tempting for at least two reasons: one of them, perhaps the strongest, was that the proof of this theorem seemed to be relatively easy...