SOLUTION OF A NONLINEAR INTEGRAL EQUATION
USING A NEW THREE-STEP ITERATION
Yunus Atalan1, Vatan Karakaya2
Department of Mathematics, Yıldız Technical University, İstanbul/TURKEY
yunus_atalan@hotmail.com
1
Department of Mathematical Engineering, Yıldız Technical University, İstanbul/TURKEY
vkkaya@yahoo.com
2
Abstract: In this presentation, we introduce a new three step iteration
process and show that this iteration process strongly converges to the
unique fixed point of contraction mappings. Furthermore, we obtain this
iteration process is equivalent to Mann iteration method and converges
faster than Picard-S iterative scheme. Also, we create a table and graphics
to support this result. Moreover, we show that this iteration method can be
used to solve a nonlinear integral equation. Finally, a data dependence
result for the solution of this integral equation is proven.
Keywords: Three step iteration, strong convergence, rate of convergence,
data dependence integral equation.
References:
[1]
F. Gursoy, V. Karakaya, “A Picard-S hybrid type iteration method for
solving a differential equation with retarded argument”, arXiv preprint
arXiv:1403.2546 (2014).
[2]
M. Abbas, T. Nazir, “A new faster iteration process applied to
constrained minimization and feasibility problems”, Matematicki
Vesnik, 66(2014), 223.
[3]
R. Chugh, V. Kumar, S. Kumar, “Strong Convergence of a New Three
Step Iterative Scheme in Banach Spaces”, American Journal of
Computational Mathematics, 2(2012), 345-357.
[4]
V. Berinde, “On the approximation of fixed points of weak contractive
mappings”, Carpathian J. Math, 19(2003), 7-22.