SavedAdd your journal

Journals / Mathematical Sciences and Applications E-Notes / 2022 / Cilt: 10 - Sayı: 1

On the Existence of the Solutions of A Nonlinear Fredholm Integral Equation in Hölder Spaces

Merve TEMİZER ERSOY
Pages
16–26
Publication Date
2022-03-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In the last section, we show the efficiency of this approach on one numerical example.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, we prove the theorem concerning the existence of the solutions for some nonlinear integral equations.
📊
Key Findings & Data:Our work is more general than the previous works in [1-3].
💡
Conclusion & Impact:In the last section, we show the efficiency of this approach on one numerical example.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hölder condition · Fredholm integral equation · Schauder fixed point theorem

Abstract

In this article, we prove the theorem concerning the existence of the solutions for some nonlinear integral equations. As an application, we investigate the problem of existence of solutions of Fredholm integral equations using the technique of relative compactness in conjunction with fixed point theorem. Our solutions are placed in the space of functions satisfying the Hölder condition. Our work is more general than the previous works in [1-3]. In the last section, we show the efficiency of this approach on one numerical example.

🔖

Cite This Article

ERSOY, M. T. (2022). On the Existence of the Solutions of A Nonlinear Fredholm Integral Equation in Hölder Spaces. Mathematical Sciences and Applications E-Notes, Cilt: 10 - Sayı: 1, 16–26. https://ajindex.com/articles/690664

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Banas ́, J., Nalepa, R.:On the space of functions with growths tempered by a modulus of continuity and its applications. J. Funct. Space Appl. 13 pages, (2013). doi:
  2. Caballero, J., Abdalla, M., Sadarangani, K.: Solvability of a quadratic integral equation of Fredholm type in Hölder spaces. Electron. J. Differ. Eq. 31, 1–10 (2014)
  3. Peng, S., Wang, J., Chen, F.: A Quadratic integral equation in the space of funtions with tempered moduli of continuity. J. Appl. Math. and Informatics. 33, No. 3–4, 351–363 (2015)
  4. Banas ́, J., Chlebowicz, A.: On an elementary inequality and its application in theory of integral equations. Journal of Mathematical Inequalities. 11 (2), 595–605 (2017)
  5. Caballero, M. J., Nalepa, R., Sadarangani, K.: Solvability of a quadratic integral equation of Fredholm type with Supremum in Hölder Spaces. J. Funct. Space Appl. 7 pages, (2014)
  6. Kulenovic, M. R. S.: Oscillation of the Euler differential equation with delay. Czech.Math. J. 45, 1–16 (1995)
  7. Mures ̧an, V.: On a class of Volterra integral equations with deviating argument. Studia Univ.Babes-Bolyai Math. 44, 47–54 (1999)
  8. Mures ̧an, V.: Volterra integral equations with iterations of linear modification of the argument. Novi Sad J. Math. 33 (2), 1–10 (2003)
  9. Schauder, J.: Der Fixpunktsatz in Funktionalriiumen. Studia Math. 2, 171–180 (1930)
  10. López, B., Harjani, J., Sadaragani, K.: Existence of positive solutions in the space of Lipschitz functions to a class of fractional differential equations of arbitrary order. Racsam, 112, 1281–1294 (2018)
  11. Bacotiu, C.: Volterra-Fredholm nonlinear systems with modified argument via weakly Picard operators theory. Carpathian J. Math. 24, 1–19 (2008)
  12. Benchohra, M., Darwish, M. A.: On unique solvability of quadratic integral equations with linear modification of theargument. Miskolc Math. Notes. 10, 3–10 (2009)
  13. Dobritoiu, M.: Analysis of a nonlinear integral equation with modified argument from physics. Int. J. Math. Models 891–937 (1971)
  14. Kato, T., Mcleod, J. B.: The functional-differential equation y′(x) = ay(λx) + by(x). Bull. Amer. Math. Soc. 77 (6), [15] Lauran, M.: Existence results for some differential equations with deviating argument. Filomat. 25, 21–31 (2011)
  15. Mures ̧an,V.:Afunctional-integralequationwithlinearmodificationoftheargumentviaweaklyPicardoperators.Fixed Point Theory. 9, 189–197 (2008)
  16. Mures ̧an, V.: A Fredholm-Volterra i