On Iteration Method to The Solution of More General Volterra Integral Equation in Two Variables and a Data Dependence Result

Yıl 2021, , 313 - 318, 27.09.2021

Samet Maldar

https://doi.org/10.18466/cbayarfbe.837062

Öz

Fixed point theory is one of the most important theories and has been studied extensively by researchers in many disciplines. One of these studies is its application to integral equations. In this work, we have shown that the iteration method given in [12] converges to the solution of the more general Volterra integral equation in two variables by using Bielecki’s norm. Also, a data dependence result for the solution of this integral equation has been proven.

Anahtar Kelimeler

convergence, data dependence, integral equation, iteration method

Kaynakça

• 1. Lungu, N. ve Rus, I.A. 2009. On a Functional Volterra-Fredholm Integral Equation via Picard Operator. Journal of Mathematical Inequalities; 3 (4): 519-527.
• 2. Bielecki, A., 1956. Un Remarque sur L’application de la Méthode de Banach-Cacciopoli-Tikhonov dans la Théorie de L’equation s= f (x, y, z, p, q). Bull. Acad. Polon. Sci. Sér. Sci. Math. Phys. Astr; 4: 265-268.
• 3. Hadizadeh, M., and Asgary, M. 2005. An efficient numerical approximation for the linear class of mixed integral equations. Applied mathematics and computation; 167(2), 1090-1100.
• 4. Gursoy, F. 2014. Applications of normal S-iterative method to a nonlinear integral equation. The Scientific World Journal; 2014, 1-5.
• 5. Garodia, C., and Uddin, I. (2018). Solution of a nonlinear integral equation via new fixed point iteration process. arXiv preprint arXiv:1809.03771.
• 6. Ilea, V., and Otrocol, D. 2020. Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances. Symmetry, 12(9), 1554.
• 7. Craciun, C.., and Serban, M. A. 2011. A nonlinear integral equation via Picard operators. Fixed point theory; 12(1), 57-70.
• 8. Atalan, Y. 2019. İteratif Yaklaşım Altında Bir Fonksiyonel-İntegral Denklem Sınıfının Çözümünün İncelenmesi. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 9(3), 1622-1632.
• 9. Atalan, Y., and Karakaya, V. 2017. Iterative Solution of Functional Volterra-Fredholm Integral Equation with Deviating Argument. Yokohama Publishers; 18(4), 675-684.
• 10. Ciplea, S. A., Lungu, N., Marian, D., and Rassias, T. M. 2020. On Hyers-Ulam-Rassias stability of a Volterra-Hammerstein functional integral equation. arXiv preprint arXiv:2001.07760.
• 11. Abdou, M. A., Soliman, A. A., and Abdel–Aty, M. A. (2020). On a discussion of Volterra–Fredholm integral equation with discontinuous kernel. Journal of the Egyptian Mathematical Society, 28(1), 1-10.
• 12. Maldar, S. 2020. Yeni Bir İterasyon Yöntemi İçin Yakınsaklık Hızı. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 10(2), 1263-1272.
• 13. Soltuz S. M. and Grosan T. 2008. Data dependence for Ishikawa iteration when dealing with contractive like operators. Fixed Point Theory Appl. 2008 (2008), 1-7.