Main Article Content

Abstract

In this work, we prove the existence of solutions for a tripled systemof integral equations using some new results of fixed point theory associated withmeasure of noncompactness. These results extend the results in some previousworks. Also, the condition under which the operator admits fixed points is moregeneral than the others in literature.

Keywords

Measure of noncompactness Fixed point System of integral equations.

Article Details

Author Biographies

Vatan Karakaya, Yıldız Technical University

Department of Mathematical Engineering

Mohammad Mursaleen, Aligarh Muslim University, Aligarh 202002,

Department of Mathematics

Nour El Houda Bouzara, University of Science and Technology HouariBoumediène, Bab-Ezzouar, 16111 Algies,

Faculty of Mathematics,

Derya Sekman, Faculty of Arts and Sciences, Ahi EvranUniversity, 40100 Kirsehir

Department of Mathematics
How to Cite
Karakaya, V., Mursaleen, M., Bouzara, N. E. H., & Sekman, D. (2019). Measure of Non-Compactness in The Study of Solutions for A System of Integral Equations. Journal of the Indonesian Mathematical Society, 25(1), 62–74. https://doi.org/10.22342/jims.25.1.554.62-74

References

  1. Aghajani, A., Allahyari, R., Mursaleen, M., "A Generalization Of Darbos Theorem With Application To The Solvability Of Systems Of Integral Equations", Comput. Math. Appl. 260 (2014), 6877.
  2. Aghajani, A., Banas, J., Jalilian, Y., "Existence Of Solutions For A Class Of Nonlinear Volterra Singular Integral Equations", Comput. Math. Appl. 62 (2011), 12151227.
  3. Aghajani, A., Haghighi, A.S., "Existence Of Solutions For A System Of Integral Equations Via Measure Of Noncompactness", Novi Sad J. Math. 44(1) (2014), 59-73.
  4. Aghajani, A., Jalilian, Y., "Existence Of Nondecreasing Positive Solutions For A System Of Singular Integral Equations", Mediterr. J. Math. 8 (2011), 563576.
  5. Akmerov, R.R., Kamenski, M.I., Potapov, A.S., Rodkina, A.E., Sadovskii, B.N., Measures Of Noncompactness and Condensing Operators, Birkhauser-Verlag, Basel, 1992.
  6. Arab, R., Allahyari, R., Haghighi, A., "Existence Of Solutions Of In nite Systems Of Integral Equations In Two Variables Via Measure Of Noncompactness", Applied Mathematics and Comput. 246 (2014), 283291.
  7. Bana´s, J., "Measures Of Noncompactness In The Study Of Solutions Of Nonlinear Di¤erential and Integral Equations", Cent. Eur. J. Math. 10(6) (2012), 20032011.
  8. Bana´s, J., "On Measures Of Noncompactness In Banach Spaces", Comment. Math. Univ. Carolin. 21 (1980), 131143.
  9. Bana´s, J., Goebel, K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, New York, 1980.
  10. Bana´s, J., Mursaleen, M., Sequence Spaces and Measures of Noncompactness with Applications to Di¤ erential and Integral Equations, Springer, 2014.
  11. Bana´s, J., Rzepka, R., "An Application Of A Measure of Noncompactness In The Study Of Asymptotic Stability", Appl. Math. Lett. 16 (2003), 16.
  12. Berinde, V., Borcut, M., "Tripled Fixed Point Theorems For Contractive Type Mappings In Partially Ordered Metric Spaces", Nonlinear Anal. TMA 74 (2011), 4889-4897.
  13. Chang, S.S., Cho, Y.J., Huang, N.J., "Coupled Fixed Point Theorems With Applications", J. Korean Math. Soc. 33 (1996), 575585.
  14. Deepmala, Pathak, H.K., "Study on Existence of Solutions For Some Nonlinear Functional-Integral Equations With Applications", Math. Commun. 18 (2013), 97-107.
  15. Karakaya, V., Bouzara, N.E.H., Dogan, K., Atalan, Y. "Existence of Tripled Fixed Points For A Class of Condensing Operators in Banach Spaces", The Scienti c World Journal 2014 (2014), 9 pages, Article ID 541862, doi:10.1155/2014/541862.
  16. Kuratowski, K., "Sur Les Espaces Complets", Fund. Math. 5 (1930), 301309.
  17. Mursaleen, M., Mohiuddine, S.A., "Applications of Measures of Noncompactness to The In nite System of Differential Equations in lp Space", Nonlinear Anal. 75 (2012), 21112115.
  18. Shaochun, J., Gang, L., "A Uni ed Approach to Nonlocal Impulsive Di¤erential Equations With The Measure of Noncompactness", Advances in Difference Equations (2012), 1-14.
  19. Sikorska, A., "Existence Theory For Nonlinear Volterra Integral and Di¤erential Equations", J. of lnequal. & Appl. 6 (2001), 6325-338.