An Extension of the Contraction Principle [PDF]
Journal of Theoretical Probability, 2004 The ``contraction principle'' is about large deviations; the basic definitions figure in [\textit{A. Dembo} and \textit{O. Zeitouni}, ``Large deviation techniques and applications''. 2nd ed. (1998; Zbl 0896.60013)]. Its statement is (C). Let \((X_{n})\) satisfy the large deviation principle with good rate function \(I\) (defined on the metric space \({\
openaire +2 more sources
Generalized contraction principle under relatively weaker contraction in partial metric spaces
Advances in Difference Equations, 2019 In this paper, we introduce the concept of a generalized weak (ϕ,R) $(\phi,\mathcal{R})$-contraction and employ this to prove some fixed point results for self-mappings in partial metric spaces endowed with a binary relation R $\mathcal{R}$.
Atiya Perveen +2 more
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Projective metrics and contraction principles for complex cones [PDF]
, 2008 In this article, we consider linearly convex complex cones in complex Banach spaces and we define a new projective metric on these cones. Compared to the hyperbolic gauge of Rugh, it has the advantage of being explicit, and easier to estimate.
Dubois, Loic
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Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement [PDF]
, 2009 The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face ...
Baume, Jean-Pierre +2 more
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A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle
Fixed Point Theory and Applications, 2004 We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces.
Jacek Jachymski
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Krasnoselskii's theorem in generalized Banach spaces and application
Electronic Journal of Qualitative Theory of Differential Equations, 2012 The purpose of this paper is to extend Krasnoselskii's fixed point theorem to the case of generalized Banach spaces for singlevalued and multivalued operators.
I. R. Petre, Adrian Petrusel
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Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation [PDF]
, 2017 We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are ...
Esfahani, Amin, Mohammadi, Hamideh B.
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A generalization of contraction principle
International Journal of Mathematics and Mathematical Sciences, 1981 In this paper, a generalized mean value contraction is introduced. This contraction is an extension of the contractions of earlier researchers and of the generalized mean value non-expansive mapping.
K. M. Ghosh
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Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions [PDF]
Opuscula Mathematica, 2013 This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order \(q \in (1,2]\) with nonlocal and integral boundary conditions.
Sotiris K. Ntouyas
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Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization [PDF]
, 2014 Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via convex optimization.
Manchester, Ian R. +1 more
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