Research article

Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1<p<\infty)$ and $c_{0}$

  • Received: 25 November 2019 Accepted: 10 April 2020 Published: 21 April 2020
  • MSC : 47H09, 47H10

  • In this paper, by applying the technique of measure of noncompactness and a new generalization of Darbo's theorem, we study the existence of solutions for an infinite system of integral equations in two variables. The obtained results extend and generalize some related results in previous work. Finally, some examples are included to ascertain the usefulness of the outcome.

    Citation: Ayub Samadi, M. Mosaee Avini, M. Mursaleen. Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1<p<\infty)$ and $c_{0}$[J]. AIMS Mathematics, 2020, 5(4): 3791-3808. doi: 10.3934/math.2020246

    Related Papers:

  • In this paper, by applying the technique of measure of noncompactness and a new generalization of Darbo's theorem, we study the existence of solutions for an infinite system of integral equations in two variables. The obtained results extend and generalize some related results in previous work. Finally, some examples are included to ascertain the usefulness of the outcome.


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    [4] A. Aghajani, M. Mursaleen, A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta Math. Sci., 35B (2015), 552-566.
    [5] A. Das, B. Hazarika, M. Mursaleen, Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in $\ell_{p}(1 < p < \infty)$, Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales, 113 (2017), 31-40.
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    [9] B. Rzepka, Solvability of a nonlinear Volterra-Stieltjes integral equation in the class of bounded and continuous functions of two variables, Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales, 112 (2018), 311-329.
    [10] K. Kuratowski, Sur les espaces completes, Fund. Math., 15 (1934), 301-335.
    [11] J. Banas, K. Goebel, Measures of Noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, 60, Marcel Dekker, New York, 1980.
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    [13] A. Samadi, Applications of measure of noncompactness to coupled fixed points and systems of integral equations, Miskolc Math. Notes, 19 (2018), 537-553. doi: 10.18514/MMN.2018.2532
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    [15] D. O'Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Academic, Dordrecht, 1998.
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