پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 713 |
| تعداد مقالات | 10,263 |
| تعداد مشاهده مقاله | 72,057,809 |
| تعداد دریافت فایل اصل مقاله | 63,817,723 |
Construction of compact-integral operators on $C^\infty(\Bbb{R}_+)$ and $C^n(\Bbb{R}_+)$ with application in the study of functional integro-differential equations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 29، دوره 15، شماره 10، دی 2024، صفحه 377-389 اصل مقاله (541.01 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.26265.3280 | ||
| نویسندگان | ||
| Asghar Allahyari1؛ Hojjatollah Amiri Kayvanloo2؛ Mohammad Mursaleen3، 4؛ Ali Shole Haghighi2؛ Mohammad Davarpanah5؛ Reza Allahyari* 2 | ||
| 1Department of Mathematics, Tabas Branch, Islamic Azad University, Tabas, Iran. | ||
| 2Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. | ||
| 3Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India | ||
| 4Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan | ||
| 5Department of Mathematics, Ferdows Branch, Islamic Azad University, Ferdows, Iran. | ||
| تاریخ دریافت: 21 بهمن 1400، تاریخ بازنگری: 06 مهر 1402، تاریخ پذیرش: 28 مهر 1402 | ||
| چکیده | ||
| In this brief note, we present a fixed point theorem in the Fr$\acute{e}$chet space. Also we study a new family of measures of noncompactness on $C^\infty(\Bbb{R}_+)$ and $C^n(\Bbb{R}_+)$ and we investigate the construction of compact-integral operators on $C^\infty(\Bbb{R}_+)$ and $C^n(\Bbb{R}_+)$. Finally, we provide various examples which illustrate the existence of solutions for a wide variety of functional integral-differential equations. | ||
| کلیدواژهها | ||
| Family of measures of noncompactness؛ condensing operators؛ integral-differential equations | ||
| مراجع | ||
|
[1] R.P. Agarwal, M. Benchohra, and D. Seba, On the application of measure of noncompactness to the existence of solutions for fractional differential equations, Results Math. 55 (2009), 221–230. [2] R. Agarwal, M. Meehan, and D. O’Regan, Fixed Point Theory and Applications, Cambridge University Press, 2004. [3] A. Aghajani, J. Banas, and Y. Jalilian, Existence of solutions for a class of nonlinear Volterra singular integral equations, Comput. Math. Appl. 62 (2011), 1215–1227. [4] A. Aghajani, R. Allahyari, and M. Mursaleen, A generalization of Darbo’s theorem with application to the solvability of systems of integral equations, J. Comput. Appl. Math. 260 (2014), 68–77. [5] A. Aghajani, M. Mursaleen, and A. Shole Haghighi, Fixed point theorems for Meir-Keeler condensing operators via measure of noncompactness, Acta Math. Sci. 35B (2015), no. 3, 552–566. [6] R. Arab, The existence of fixed points via the measure of non-compactness and its application to functional integral equations, Mediterr. J. Math. 13 (2016), 759–773. [7] A. Ayad, Spline approximation for first order Fredholm delay integro-differential equations, Int. J. Comput. Math. 70 (1999), no. 3, 467–476. [8] J. Banas, Measures of noncompactness in the study of solutions of nonlinear differential and integral equations, Cent. Eur. J. Math. 10 (2012), no. 6, 2003–2011. [9] M. Benchohra, Z. Bouteffal, J. Henderson, and S. Litimein, Measure of noncompactness and fractional integro-differential equations with state-dependent nonlocal conditions in Frechet spaces, Aims Math. 5 (2020), no. 1, 15–25. [10] F. Bloom, Asymptotic bounds for solutions to a system of damped integro-differential equations of electromagnetic theory, J. Math. Anal. Appl. 73 (1980), no. 2, 524–542. [11] G. Darbo, Punti uniti in trasformazioni a codominio non compatto, Rend. Sem. Mat. Uni. Padova. 24 (1955), 84–92. [12] S. Djebali and K. Hammache, Fixed point theorems for nonexpansive maps in Banach spaces, Nonlinear Anal. 73 (2010), 3440–3449. [13] J. Garcia-Falset, Existence of fixed points and measures of weak noncompactness, Nonlinear Anal. 71 (2009), 2625–2633. [14] D. Guo, Existence of solutions for nth-order integro-differential equations in Banach spaces, Comput. Math. Appl. 41 (2001), 597–606. [15] S. Hadi Bonab, V. Parvaneh, and J. Rezaei Roshan, The solvability of an iterative system of functional integral equations with self-composition of arbitrary order, submitted. [16] H. Hosseinzadeh, H. Isik, S. Hadi Bonab, and R. George, Coupled measure of noncompactness and functional integral equations, Open Math. 20 (2022), 38–49. [17] K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301–309. [18] B. Mohammadi, V. Parvaneh, and H. Hosseinzadeh, Some Wardowski-Mizogochi-Takahashi-Type generalisations of the multi-valued version of Darbo’s fixed point theorem with applications, Int. J. Nonlinear Anal. Appl. 2023, 10.22075/ijnaa.2023.23057.2470 [19] M. Mursaleen, V. Rakocevic, A survey on measures of non-compactness with some applications in infinite systems of differential equations, Aequ. Math. 96 (2022), 489-–514. [20] V. Parvaneh, S. Banaei, J.R. Roshan, and M. Mursaleen, On tripled fixed point theorems via measure of noncompactness with applications to a system of fractional integral equations, Filomat 35 (2021), no. 14, 4897–4915. [21] M. Rabbani, R. Arab, B. Hazarika, and N. Aghazadeh, Existence of solution of functional integral equations by measure of noncompactness and sinc interpolation to find solution, Fixed Point Theory 23 (2022), no. 1, 331–334. [22] J.R. Roshan, Existence of solutions for a class of system of functional integral equation via measure of noncompactness, J. Comput. Appl. Math. 313 (2017), 129–141. | ||
|
آمار تعداد مشاهده مقاله: 1,466 تعداد دریافت فایل اصل مقاله: 1,080 |
||