Yazar "Karakaya, Vatan" seçeneğine göre listele

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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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    New matrix domain derived by the matrix product
    (UNİV NIS, 2016) Karakaya, Vatan; Şimşek, Recep; Doğan, Kadri
    In this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the alpha-, beta- and gamma- duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c, l(infinity).
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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.
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    Some fixed point results for continuous functions on an arbitrary intervals
    (Yıldız Teknik Üniversitesi, 2019) Doğan, Kadri; Gürsoy, Faruk; Karakaya, Vatan
    In this paper, we first give a necessary and sufficient condition for convergence of Picard-S iteration process to a fixed point of continuous functions on an arbitrary interval and prove equivalence of Picard-S and P iterative processes. We also compare the rate of convergence between Picard-S and some others iteration processes in the literature. Finally, some numerical examples for comparing the rate of convergence of those methods are also given.
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    Some fixed point results in the generalized convex metric spaces
    (Turkic World Mathematical Society, 2020) Doğan, Kadri; Gürsoy, Faruk; Karakaya, Vatan
    In this study, we introduce a new three step iteration process and show that the iteration process converges to the unique fixed point by two theorems under different conditions of contractive mappings on the generalized G- convex metric spaces. Also, we investigate data dependence result for this iterative process in the generalized G- convex metric spaces.
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    Some new results on convergence, stability and data dependence in n-normed spaces
    (Ankara Üniversitesi, 2020) Doğan, Kadri; Gürsoy, Faruk; Karakaya, Vatan; Khan, Safeer Hussain
    We introduce a new contractive condition and a new iterativemethod innnormed space setting. We employ both of these to study con-vergence, stability, and data dependence. The results presented here extendand improve some recent results announced in the existing literature