Marlène Frigon

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In this paper, we present fixed point results for generalized contractions defined on a complete gauge space E. Also, we consider families of generalized contractions {f t : X → E} t∈[0,1] where X ⊂ E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some f t 0 imply the existence of a fixed point for(More)
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or(More)
Copyright q 2011 Yonghong Yao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We use strongly pseudocontraction to regularize the following ill-posed monotone variational inequality:(More)
Recommended by Marlene Frigon We define a weaker Meir-Keeler type function and establish the fixed point theorems for a weaker Meir-Keeler type ψ-set contraction in metric spaces. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided(More)
and Applied Analysis 3 In the last section of this paper,we study the system 1.2 . Again, we introduce a notion of solution-tube of 1.2 which generalizes the notion of lower and upper solutions used by Atici et al. 8 . This notion generalizes also condition 1.5 and the notion of solution-tube of systems of second-order differential equations introduced in(More)
Rassias introduced the following equality ∑n i,j 1 ‖xi − xj‖ 2n ∑n i 1 ‖xi‖, ∑n i 1 xi 0, for a fixed integer n ≥ 3. Let V,W be real vector spaces. It is shown that, if a mapping f : V → W satisfies the following functional equation ∑n i,j 1 f xi−xj 2n ∑n i 1 f xi for all x1, . . . , xn ∈ V with ∑n i 1 xi 0, which is defined by the above equality, then the(More)