Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41220150401Application of measures of noncompactness to infinite system of linear equations in sequence spaces519527627ENA.AlotaibiDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaM.MursaleenDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, India, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaS. A.MohiuddineDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia, and,
Operator Theory and its Applications Research Group, King Abdulaziz University, Jeddah, Saudi ArabiaJournal Article20140102G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
http://bims.iranjournals.ir/article_627_feb3b9c527fe3048301249148495a3d7.pdf