Applications of measure of noncompactness for the solvability of an infinite system of second order differential equations in some integrated sequence spaces

• Das, Rituparna ^[2] ; Sapkota, Niraj ^[1]
  1. [1] Sikkim Manipal University

     Sikkim Manipal University

     India

     
  2. [2] Pandu College
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 2, 2021, págs. 573-592
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-2021-02-0032
• Enlaces
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• Resumen

  • The aim of this paper is to study the infinite system of second order differential equations along with the given boundary conditions for its solvability in some integrated sequence spaces. The result is achieved with the analytical tool namely the measure of noncompactness along with the idea of Meir-Keeler condensing operator and provides the realization of the sufficient conditions for the existence results in these Banach Sequence spaces. We also illustrate the results with examples.

• Referencias bibliográficas
  • K. Kuratowski, “Sur les espaces complets”, Fundamenta mathematicae, vol.15, no. 1, pp. 301-309, 1930. [On line]. Available: https://bit.ly/3cxtQr5
  • G. Darbo, “Punti uniti in transformazioni a condominio non compatto”, Rendiconti del Seminario Matematico della Università di Padova, vol....
  • L. S. Goldenstein and A. S. Markus, “On a measure of noncompactness of bounded sets and linear operators”, Studies in algebra and mathematical...
  • A. Meir and E. Keeler, “A theorem on contraction mappings”, Journal of mathematics analysis and applications, vol. 28, no. 1, 1969, pp. 326-329,...
  • G. Goes and S. Goes, “Sequences of bounded variation and sequences of Fourier coefficients. I”, Mathematische zeitschrift, vol. 118, no. 2,...
  • V. Istrăţescu, “On a measure of noncompactness”, Bulletin mathématique de la Société des Sciences Mathématiques de la République Socialiste...
  • J. Banaś and K. Goebel, Measures of noncompactness in Banach spaces. New York, NY: Marcel Dekker, 1980.
  • K. P. Persidskii, “Countable systems of differential equations and stability of their solutions”, Izvestiya Akademii Nauk Kazakh SSR, vol....
  • K. P. Persidskii, “Countable systems of differential equations and stability of their solutions III: fundamental theorems on stability of...
  • K. P. Persidskii, “Infinite system of differential equations”, Izvestiya Akademii Nauk Kazakh SSR Alma Ata Differential Equations. Nonlinear...
  • J. Banaś, “Measures of noncompactness in the space of continuous tempered functions”, Demonstratio mathematica, vol. 14, no. 1, pp. 127-133,...
  • R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, and B. N. Sadovskii, Measures of noncompactness and condensing operators, operator...
  • J. Banaś and A. Martinon, “Some properties of the Hausdorff distance in metric spaces”, Bulletin of the Australian Mathematical Society, vol....
  • J. Banaś and A. Martinon, “Measures of noncompactness in Banach sequence spaces”, Mathematica Slovaca, vol.42, no. 4, pp. 497-493, 1992. [On...
  • J. Banaś and M.Lecko, “Solvability of infinite systems of differential equations in Banach sequence spaces”, Journal of computational and...
  • D. G. Duffy, Greens functions with applications. Boca Raton, FL: Chapman & Hall/CRC, 2001.
  • R. P. Agarwal, M. Benchohra, and D. Seba, “On the application of measure of noncompactness to the existence of solutions for fractional differential...
  • M. Mursaleen and A. K. Noman, “Compactness by the Hausdorff measure of noncompactness”, Nonlinear analysis: theory, methods & applications,...
  • M. Mursaleen and S. A. Mohiuddine, “Applications of measures of noncom-pactness to the infinite system of differential equations in ℓp spaces”,...
  • J. Banaś, and M. Mursaleen, Sequence spaces and measures of non-compactness with applications to differential and integral equations. New...
  • A. Aghajani, R. Allahyari, and M. Mursaleen, “A generalization of Darbos theorem with application to the solvability of systems of integral...
  • A. Aghajani, M. Mursaleen, and A. S. Haghighi, “Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness”,...
  • A. Alotaibi, M. Mursaleen, and S. A. Mohiuddine, “Application of measure of noncompactness to infinite system of linear equations in sequence...
  • M. Kirişci, “Integrated and differentiated sequence spaces”, Journal of nonlinear analysis and application, vol. 2015, no. 1, pp. 2-16, 2015,...
  • M. Mursaleen and S. M. H. Rizvi, “Solvability of infinite systems of second order differential equations in c0 and ℓ1 by Meir-Keeler condensing...
  • H. M. Srivastava, A. Das, B. Hazarika, and S. A. Mohiuddine, “Existence of solutions of infinite systems of differential equations of general...
  • A. Das, B. Hazarika, and M. Mursaleen, “Application of measure of noncom-pactness for solvability of the infinite system of integral equations...
  • R. Saadati, E. Pourhadi, and M. Mursaleen, “Solvability of infinite systems of third-order differential equations in c0 by Meir-Keeler condensing...
  • B. Hazarika, R. Arab, and M. Mursaleen, “Application measure of noncompactness and operator type contraction for solvability of an infinite...