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Solvability of infinite systems of second order differential equations in $ c_0$ and $ \ell_1$ by Meir-Keeler condensing operators


Authors: M. Mursaleen and Syed M. H. Rizvi
Journal: Proc. Amer. Math. Soc. 144 (2016), 4279-4289
MSC (2010): Primary 47H09, 47H10; Secondary 34A34
DOI: https://doi.org/10.1090/proc/13048
Published electronically: March 30, 2016
MathSciNet review: 3531179
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Abstract: In this paper, we present existence results for the solution of infinite systems of second order differential equations in Banach sequence spaces $ c_0$ and $ \ell _1$ using the idea of Meir-Keeler condensing operators. We also give some examples to illustrate our results in these sequence spaces.


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Additional Information

M. Mursaleen
Affiliation: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Email: mursaleenm@gmail.com

Syed M. H. Rizvi
Affiliation: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Email: syedrizvi022@gmail.com

DOI: https://doi.org/10.1090/proc/13048
Keywords: Measure of noncompactness, Darbo's fixed point theorem, Meir-Keeler condensing operators, infinite system of differential equations
Received by editor(s): August 23, 2015
Received by editor(s) in revised form: November 26, 2015
Published electronically: March 30, 2016
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society

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