Fixed point theorems in Fréchet algebras and Fréchet spaces and applications to nonlinear integral equations

Dudek, Szymon

doi:10.2298/aadm1702340d

Cited by 27 publications

(21 citation statements)

References 12 publications

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“…Moreover, if u is a solution of problem (1)-(2), then We recall the following definition of the notion of a sequence of measures of noncompactness [17,18].…”

Section: Existence and Attractivity Resultsmentioning

confidence: 99%

“…In the sequel we will make use of the following generalization of the classical Darbo fixed point theorem for Fréchet spaces. 17,18]). Let Ω be a nonempty, bounded, closed, and convex subset of a Fréchet space F and let V : Ω → Ω be a continuous mapping.…”

Section: Definition 46mentioning

confidence: 99%

“…Simple computations show that all conditions of Theorem 5.2 are satisfied. It follows that the problem (17) has at least one bounded solution defined on R + .…”

Section: Examplementioning

confidence: 99%

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Fractional ${q}$-difference equations on the half line

Abbas¹,

Benchohra²,

Laledj³

et al. 2020

Arch. Math. (Brno)

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This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional q-difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.

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“…Moreover, if u is a solution of problem (1)-(2), then We recall the following definition of the notion of a sequence of measures of noncompactness [17,18].…”

Section: Existence and Attractivity Resultsmentioning

confidence: 99%

Section: Definition 46mentioning

confidence: 99%