Solvability of the infinite system of integral equations in two variables in the sequence spaces c0 and l1

In this article, we establish the existence of solution of infinite systems of integral equations in two variables in the sequence spaces c0 and l1 by using Meir–Keeler condensing operators. We explain the results with the help of simple examples.

[1]  Mohammad Mursaleen,et al.  Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations , 2014 .

[2]  Mohammad Mursaleen,et al.  A generalization of Darbo's theorem with application to the solvability of systems of integral equations , 2014, J. Comput. Appl. Math..

[3]  Mohammad Mursaleen,et al.  Applications of measures of noncompactness to the infinite system of differential equations in ℓp spaces , 2012 .

[4]  Hari M. Srivastava,et al.  Application of measures of noncompactness to the infinite system of second-order differential equations in ℓp$\ell_{p}$ spaces , 2016 .

[5]  C. Kuratowski,et al.  Sur les espaces complets , 1930 .

[6]  Ehsan Pourhadi,et al.  Application of measure of noncompactness to $\ell_{1}$-solvability of infinite systems of second order differential equations , 2015 .

[7]  Gabriele Darbo,et al.  Punti uniti in trasformazioni a codominio non compatto , 1955 .

[8]  S. Banach Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[9]  M. Mursaleen,et al.  Solvability of infinite systems of second order differential equations in ₀ and ℓ₁ by Meir-Keeler condensing operators , 2016 .

[10]  Józef Banaś,et al.  Measures of Noncompactness in Banach Spaces , 1980 .

[11]  Mohammad Mursaleen,et al.  FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS ∗ , 2015 .

[12]  Józef Banaś,et al.  Solvability of infinite systems of differential equations in Banach sequence spaces , 2001 .

[13]  M. Mursaleen,et al.  Infinite System of Differential Equations in Some Spaces , 2012 .

[14]  Emmett B. Keeler,et al.  A theorem on contraction mappings , 1969 .

[15]  Reza Arab,et al.  Existence of solutions of infinite systems of integral equations in two variables via measure of noncompactness , 2014, Appl. Math. Comput..

[16]  Mohammad Mursaleen,et al.  Application of measures of noncompactness to infinite system of linear equations in sequence spaces , 2015 .