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Existence of solutions of infinite systems of quadratic integral equations of Hammerstein type on an unbounded interval in Fréchet spaces | ||
Journal of New Researches in Mathematics | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 20 اردیبهشت 1399 | ||
نوع مقاله: research paper | ||
نویسندگان | ||
reza allahyari 1؛ mohsen Hossein Zadeh Moghaddam1؛ Asghar Allahyari2؛ ali shole haghighi3 | ||
1Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. | ||
2Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran. | ||
3Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran. | ||
چکیده | ||
Measures of noncompactness are very useful tools in the theory of operator equations in Banach and Fréchet spaces. They are frequently used in the theory of functional equations, including ordinary differential equations, equations with partial derivatives, integral equations and integro-differential equations, optimal control theory, etc. In particular, the fixed point theorems derived from them have many applications. In this paper, we present some fixed point theorems for condensing operators on Fréchet spaces by using the technique of measures of noncompactness together with the Tychonoff fixed point theorem. Moreover, we introduce a new measure of noncompactness on the countable Cartesian product of Banach spaces, and then study the problem of the existence of solutions for an infinite system of quadratic integral equations of Hammerstein type on an unbounded interval which includes several classes of nonlinear integral equations of Hammerstein type. Finally, an example is presented to show the efficiency of our results. | ||
کلیدواژهها | ||
Measure of noncompactness؛ Fréchet space؛ Tychonoff fixed point theorem؛ Infinite systems of equations؛ Quadratic integral equations | ||
آمار تعداد مشاهده مقاله: 185 |