Applications of measures of noncompactness to the infinite system of differential equations in spaces

Mursaleen, M.; Mohiuddine, S. A.

doi:10.1016/j.na.2011.10.011

Cited by 145 publications

(61 citation statements)

References 9 publications

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“…There are some studies that treat infinite systems of O.D.E. 's and their applications, here we refer [3,4,[21][22][23]. It is worthwhile to note that the technique that we have been used for our aim, can be applied whenever we need to compile a set of Banach function spaces, which can happen in other contexts not studied here.…”

Section: Mjommentioning

confidence: 99%

On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations

Galdames-Bravo

2014

Mediterr. J. Math.

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In the present paper we give some necessary conditions that satisfy the solutions of an infinite system of ordinary differential equations. We investigate the behavior of the solutions of a general system of equations, regarding the norm of a Banach function space based on a vector measure. To this aim we construct a vector measure by an standard procedure. Assuming that the solution of each individual equation of the system belongs to a Banach function space based on scalar measures we deduce, with natural conditions, that a solution of such system belongs to a Banach function space based on a vector measure. We also give an example of a system of non-linear Bernoulli equations and show the relation with an equation involving the integral operator.Mathematics Subject Classification. Primary 46G10; Secondary 47N20, 46N20.

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Section: Mjommentioning

confidence: 99%

On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations

Galdames-Bravo

2014

Mediterr. J. Math.

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“…It is worthwhile mentioning that the problem of existence of solutions of an infinite system of ordinary differential equations was also studied in [5,11,18,19,21], among others.…”

Section: Existence Of Solutions Of An Infinite System Of Ordinary Difmentioning

confidence: 99%

Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

Banaś

2012

Open Mathematics

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“…On the other hand, measures of noncompactness are very useful tools in the wide area of functional analysis such as the metric fixed point theory and the theory of operator equations in Banach spaces. They are also used in the study of functional equations, ordinary and partial differential equations, fractional partial differential equations, integral and integro-differential equations, optimal control theory, etc., see [1][2][3][4][5][6][12][13][14][15][16]. In our investigations, we apply the method associated with the technique of measures of noncompactness to generalize the Darbo fixed point theorem [9] and to extend some recent results of Aghajani et al [5].…”

Section: Introductionmentioning

confidence: 99%

Some generalizations of Darbo fixed point theorem and its application

Arab¹

2017

MMN

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Abstract. Recently, B. Samet et al. (Fixed Point Theory and Appl. 2013:5, 2013, doi:10.1186/1687-1812 has introduced the concept of new contraction mappings and obtained results on the fixed point for nonlinear contractive mappings in a metric space. In the present paper, we introduce the concept of a new contraction via the measure of non-compactness on a Banach space, we obtain a few generalizations of Darbo fixed point theorem and extend some recent results of Aghajani et al. We also show the applicability of obtained results to the theory of integral equations.

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Applications of measures of noncompactness to the infinite system of differential equations in spaces

Cited by 145 publications

References 9 publications

On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations

On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations

Measures of noncompactness in the study of solutions of nonlinear differential and integral equations

Some generalizations of Darbo fixed point theorem and its application

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