04Mar 2018

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO SYSTEM OF LINEAR EQUATIONS AND INTEGRAL EQUATIONS USING BANACH FIXED-POINT THEOREM.

  • Department of Mathematics, University of Dhaka, Dhaka-1000.
  • Department of Mathematics, Jessore University of Science & Technology, Jessore-7408.
  • Department of General Educational Development, Daffodil International University, Dhaka-1000.
  • Department of Computer Science and Engineering, Dhaka International University, Dhaka-1000.
Crossref Cited-by Linking logo

Plum Print visual indicator of research metrics
  • Captures
    • Readers: 2
see details

  • Abstract
  • Keywords
  • References
  • Cite This Article as
  • Corresponding Author

In this paper, using Banach fixed-point theorem, we study the existence and uniqueness of solution for a system of linear equations. Further, we prove the existence and uniqueness of the continuous solutions of linear and non-linear Fredholm integral equations over the Banach space . Our claim is also illustrated with the applications to respective examples for proving the existence results.

  1. Agarwall R. P., Meehan M., O?Regan D., Fixed Point Theory and Applications, Cambridge University Press, 2001.
  2. Banach S., Sur less oprations dans les ensembles abstraits et leur applications aux equations integrates, Fund. Math. 3(1922), 133-181.
  3. Debnath L., Mikusinski P., Introduction to Hilbert Spaces with Applications, Elsevier, 2005.
  4. Franklin J., Methods of Mathematical Economics, Springer-Verlag, New York, 1980.
  5. Karoui A., On the Existence of Continuous Solutions of Nonlinear Integral Equations, Applied Mathematics Letters, 18(2005), 299-305.
  6. Mohensialhosseini S.A.M., Application of Fixed Point Theorem and Error Bounds, Open Access Library Journal, 1: e567(2014).
  7. Nazam M., Arshad M., On a Fixed Point Theorem with Application to Integral Equations, International Journal of Analysis, 2016, 1-7.
  8. Zeidler E., Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems, Springer-Verlag, New York, 1986.
  9. http://users.math.uoc.gr/~pamfilos/Winter2013/Rosenzweig.pdf.

[Razina Ferdausi, Akram Hossain, Mehedi Hasan and Ashraful Islam. (2018); EXISTENCE AND UNIQUENESS OF SOLUTIONS TO SYSTEM OF LINEAR EQUATIONS AND INTEGRAL EQUATIONS USING BANACH FIXED-POINT THEOREM. Int. J. of Adv. Res. 6 (Mar). 494-500] (ISSN 2320-5407). www.journalijar.com

Md. Akram Hossain
Department of Mathematics, Jessore University of Science & Technology

DOI:

Article DOI: 10.21474/IJAR01/6697      
DOI URL: https://dx.doi.org/10.21474/IJAR01/6697

Download Full Paper

Download PDF No. of Downloads: 262 | No. of Views: 751