Application of measures of noncompactness to the system of integral equations

References

• Aghajani, A., Allahyari, R., & Mursaleen, M. (2014). Generalization of Darbo’s theorem with application to the solvability of systems of integral equations. Journal of Computational and Applied Mathematics, 260, 68–10. doi:10.1016/j.cam.2013.09.039
   Web of Science ®Google Scholar
• Aghajani, A., Mursaleen, M., & Shole Haghighi, A. (2015). Fixed point theorems for meir-keeler condensing operators via measure of noncompactness. Acta Mathematica Scientia, 35, 552–566. doi:10.1016/S0252-9602(15)30003-5
   Web of Science ®Google Scholar
• Allahyari, A. (2018). The behaviour of measures of noncompactness in L∞((ℝn) with application to the solvability of functional integral equations. Revista De La Real Academia De Ciencias Exactas, Físicas Y Naturales. Serie A. Matemáticas, 112, 561–573. doi:10.1007/s13398-017-0397-4
   Google Scholar
• Bannas, J., & Goebel, K. (1980).Measure of noncompactness in banach spaces. Lecture Notes in Pure and Applied Mathematics, 60. Marcel Dekker, New York.
   Google Scholar
• Bhaskar, T. G., & Lakshmikantham, V. (2006). Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Analysis, 65, 1379–1393. doi:10.1016/j.na.2005.10.017
   Web of Science ®Google Scholar
• Darbo, G. (1955). Punti uniti in transformazioni a condominio non compatto. Rendiconti Del Seminario Matematico Della Università Di Padova, 24, 84–92.
   Google Scholar
• Darwish, M. A. (2008). On monotonic solutions of a quadratic integral equation with supremum. Dynamic Systems and Applications, 17, 539–550.
   Web of Science ®Google Scholar
• Das, A., Hazarika, B., & Mursaleen, M. (2017). Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in λp (1 < p < ∞). Revista De La Real Academia De Ciencias Exactas, Físicas Y Naturales. Serie A. Matemáticas, 113, 31–40.
   Web of Science ®Google Scholar
• Dhage, B. C., & Bellale, S. S. (2008). Local asymptotic stability for nonlinear quadratic functional integral equations. Journal of Qualitative Theory of Differential Equations, 10, 1–13.
   Google Scholar
• Hazarika, B., Arab, R., & Mursaleen, M. (2019). Applications of measure of noncompactness and operator type contraction for existence of solution of functional integral equations. Complex Analysis and Operator Theory, 13, 3837–3851. doi:10.1007/s11785-019-00933-y
   Web of Science ®Google Scholar
• Kuratowski, K. (1934). Sur les espaces completes. Fundamenta Mathematicae, 15, 301–335. doi:10.4064/fm-15-1-301-309
   Google Scholar
• Liu, L., Guo, F., Wu, C., & Wu, Y. (2005). Existence theorems of global solutions for nonlinear voltera type integral equations in banach spaces. Journal of Mathematical Analysis and Applications, 309, 638–649. doi:10.1016/j.jmaa.2004.10.069
   Web of Science ®Google Scholar
• Mohiuddine, S. A., Srivastava, H. M., & Alotaibi, A. (2016). Application of measures of noncompactness to the infinite system of second-order differential equations in λp spaces. Advances in Difference Equations, 2016(317), 1–13. doi:10.1186/s13662-016-1016-y
   Google Scholar
• Mursaleen, M., & Mohiuddine, S. A. (2012). Applications of noncompactness to the infinite system of differential equations in λp spaces. Nonlinear Anal, 75(4), 2111–2115. doi:10.1016/j.na.2011.10.011
   Google Scholar
• Mursaleen, M., & SYED, M. H. (2016). Rizvi solvability of infinite systems of second order differential equations in c0 and λ1 by meir-keeler condensing operators. Proceedings Of The American Mathematical Society, 144(10), 4279–4289. doi:10.1090/proc/13048
   Web of Science ®Google Scholar
• Olszowy, L. (1980). Solvability of infinite systems of singular integral equations in frechet space of continuous function. Computers & Mathematics with Applications, 59, 2794–2801. doi:10.1016/j.camwa.2010.01.049
   Google Scholar
• Samadi, A. (2018). Applications of measure of noncompactness to coupled fixed points and systems of integral equations. Miskolc Mathematical Notes, 19, 537–553. doi:10.18514/MMN.2018.2532
   Web of Science ®Google Scholar
• Srivastava, H. M., Das, A., Hazarika, B., & Mohiuddine, S. A. (2018). Existence of solutions of infinite systems of differential equations of general order with boundary conditions in the spaces c0 and lp via the measure of noncompactness. Mathematical Methods in the Applied Sciences, 41, 3521–3997. doi:10.1002/mma.4845
   Google Scholar
• Srivastava, H. M., Das, A., Hazarika,S, B., & Mohiuddine, A. (2019). Existence of solution for non-linear functional integral equations of two variables in banach algebra. symmetry, 11, 1–16. doi:10.3390/sym11050674
   Google Scholar