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    Comparison rate of convergence and data dependence for a new iteration method
    (Tbilisi Centre Math Sci, 2020) Maldar, Samet; Atalan, Yunus; Doğan, Kadri
    In this paper, we have defined hyperbolic type of some iteration methods. The new iteration has been investigated convergence for mappings satisfying certain condition in hyperbolic spaces. It has been proved that this iteration is equivalent in terms of convergence with another iteration method in the same spaces. The rate of convergence of these two iteration methods have been compared. We have investigated data dependence result using hyperbolic type iteration. Finally, we have given numerical examples about rate of convergence and data dependence.
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    The local and semilocal convergence analysis of new Newton-like iteration methods
    (Scientific Technical Research Council Turkey-Tubitak, 2018) Karakaya, Vatan; Atalan, Yunus; Bouzara, Nour El Houda
    The aim of this paper is to find new iterative Newton-like schemes inspired by the modified Newton iterative algorithm and prove that these iterations are faster than the existing ones in the literature. We further investigate their behavior and finally illustrate the results by numerical examples.
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    Some fixed point results for a new three steps iteration process in banach spaces
    (House Book Science-Casa Cartii Stiinta, 2017) Karakaya, Vatan; Atalan, Yunus; Doğan, Kadri; Bouzara, Nour El Houda
    In this paper, we introduce a three step iteration method and show that this method can be used to approximate fixed point of weak contraction mappings. Furthermore, we prove that this iteration method is equivalent to Mann iterative scheme and converges faster than Picard-S iterative scheme for the class of weak contraction mappings. We also present tables and three graphics to support this result. Finally, we prove a data dependence result for weak contraction mappings using this three step iterative scheme.