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    An example of data dependence result for the class of almost contraction mappings
    (University of Maragheh, 2020) Atalan, Yunus; Karakaya, Vatan
    In the present paper, we show that S* iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. Finally, we obtain a data dependence result for almost contraction mappings by using S* iteration method and in order to show validity of this result we give an example.
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    Convergence of Jungck-Kirk type iteration ethod with applications
    (University of the Punjab, 2022) Maldar, Samet; Karakaya, Vatan
    The aim of this article is to define a new Jungck-Kirk type iteration method and to examine the convergence result under appropriate conditions together with other Jungck-Kirk type iteration methods in the literature. It is also to analyze whether the newly defined iteration method is stable. In addition, it has been shown through numerical examples that the new iteration method has a better convergence rate than the others. Finally, to show the validity of convergence and stability results, some examples are given. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.
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    Investigation of some fixed point theorems in hyperbolic spaces for a three step iteration process
    (Korean Mathematical Society, 2019) Atalan, Yunus; Karakaya, Vatan
    In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give non-trivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.
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    Obtaining new fixed point theorems by using generalized banach-contraction principle
    (Erciyes Üniversitesi, 2019) Atalan, Yunus; Karakaya, Vatan
    In this study, a new three step iterative algorithm was introduced with the help of Jungck-contraction principle which is one of the remerkable generalizations of Banach-contraction principle. Also, the convergence and stability results were obtained for the pair of nonself mappings which satisfy a certain contractive condition by using this iterative algorithm in any Banach space. In addition, it was shown that the new iterative algorithm has a better convergence speed when compared the other Jungck-type iterative algorithms in the current literature, and to support this result, numerical examples were given.
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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; Doğan, Kadri; 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.