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

Ayub Samadi; M. Mosaee Avini; M. Mursaleen; Ayub Samadi; M. Mosaee Avini; M. Mursaleen

doi:10.3934/math.2020246

AIMS Mathematics

2020, Volume 5, Issue 4: 3791-3808. doi: 10.3934/math.2020246

Previous Article Next Article

Research article

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

1.
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
2.
Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan
3.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002
4.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan, India

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.
- Banach spaces $\ell_{p}$ and $c_{0}$,
- Darbo's fixed point theorem,
- measure of noncompactness,
- integral equations
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:

Abstract

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.

References

[1]	K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
[2]	S. Chandrasekhar, Radiative Transfer, Oxford University Press, London, 1950.
[3]	C. Corduneanu, Integral Equations and Applications, Cambridge University Press, Cambridge, 1991.
[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.
[6]	A. Das, B. Hazarika, R. Arab, et al. Solvability of the infinite system of integral equations in two variables in the sequence spaces c₀ and $\ell_{p}$, Jour. Comput. Appl. Math., 326 (2017), 183-192. doi: 10.1016/j.cam.2017.05.035
[7]	M. Ghasemi, M. Khanehgir, R. Allahyari, On solutions of infinite systems of integral equations in navaribles in spaces of tempered sequences $c.{\beta}_{0}$ and $l.{\beta}_{1}$, J. Math. Anal., 6 (2018), 1-16.
[8]	J. Banas, A. Dubiel, Solutions of a quadratic Volterra-Stieltjes integral equation in the class of functions converging at infinity, Electron. J. Qualitative Theory Differential Equations, 80 (2018), 1-17.
[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.
[12]	G. Darbo, Punti uniti in transformazioni a condominio non compatto, Rend. Sem. Math. Uni. Padova., 24 (1955), 84-92.
[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
[14]	J. Appell, J. Banas, M. Merentes, Bounded Variation and Around, Series in Nonlinear Analysis and Applications, 17 Walter de Gruyter, Berlin, 2014.
[15]	D. O'Regan, M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Equations, Kluwer Academic, Dordrecht, 1998.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)