The Henstock-Kurzweil-Pettis Integrals and Existence Theorems for the Cauchy Problem

Cichoń, Mieczysław; Kubiaczyk, I.; Sikorska, Aneta

doi:10.1023/b:cmaj.0000042368.51882.ab

Cited by 29 publications

(14 citation statements)

References 21 publications

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“…In this section, we investigate topological structure of the set of solutions in weak sense of following nonlinear Volterra type integral equation (1.1), x ∈ C(I, X ) and involving the Henstock-Kurzweil-Pettis integral [7,8].…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

On an integral equation under Henstock–Kurzweil–Pettis integrability

Amar

2015

Arab. J. Math.

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In this paper, we investigate the set of solutions for nonlinear Volterra type integral equations in Banach spaces in the weak sense and under Henstock-Kurzweil-Pettis integrability. Moreover, a fixed point result is presented for weakly sequentially continuous mappings defined on the function space C(K , X ), where K is compact Hausdorff and X is a Banach space. The main condition is expressed in terms of axiomatic measure of weak noncompactness. Mathematics Subject Classification

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Section: Resultsmentioning

confidence: 99%

“…Recently, for problems involving highly oscillating functions, many authors have examined the existence of solutions under Henstock-Kurzweil-Pettis integrability [1,[7][8][9]19,20,[24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

On an integral equation under Henstock–Kurzweil–Pettis integrability

Amar

2015

Arab. J. Math.

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“…The theory of generalized ordinary differential equations is extensively described in [28]. In [10] and [11], the authors extended the controlled convergence theorems and proved the existence theorems for the Cauchy problem for Banach space-valued functions under Henstock-Pettis integrability assumptions, respectively. In this section, we present a controlled convergence theorem for fuzzy Henstock-Pettis integral.…”

Section: The Existence Of Generalized Weak Solutions To Discontinuousmentioning

confidence: 99%

On the existence of generalized weak solutions to discontinuous fuzzy differential equations

Shao¹,

Gong²,

Chen³

2017

J. Nonlinear Sci. Appl.

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In this paper, by means of replacing the Lebesgue integrability of support functions with its Henstock integrability, the definitions of the Henstock-Pettis integral of n-dimensional fuzzy-number-valued functions are defined. In addition, the controlled convergence theorems for such integrals are considered. As the applications of these integrals, we provide some existence theorems of generalized weak solutions to initial value problems for the discontinuous fuzzy differential equations under the strong GH-differentiability.

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“…Some authors proposed an extension of the H-K integral, called KurzweilHenstock-Pettis integral (H-K-P integral) (see [8]) which offers an interesting possible applicability to Fourier analysis and differential equations. In this case, the solution of a Cauchy problem given by:…”

Section: Is Lebesgue Integrable ⇐⇒ Its Characteristic Function Is H-kmentioning

confidence: 99%

“…The discrete state q is known and γ q (y) is Henstock-Kurzweil-Pettis integrable 5 (see [18], [8], [33]) or NV-Integrable [10].…”

Section: Assumptionmentioning

confidence: 99%

Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability

Barbot

Benmerzouk

et al. 2011

Lecture Notes in Control and Information Sciences

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The Henstock-Kurzweil-Pettis Integrals and Existence Theorems for the Cauchy Problem

Cited by 29 publications

References 21 publications

On an integral equation under Henstock–Kurzweil–Pettis integrability

On an integral equation under Henstock–Kurzweil–Pettis integrability

On the existence of generalized weak solutions to discontinuous fuzzy differential equations

Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability

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