TY - JOUR TT - Convergence and Data Dependence Results for AK Iterative Algorithm AU - Ertürk, Müzeyyen PY - 2017 DA - September DO - 10.18466/cbayarfbe.339352 JF - Celal Bayar University Journal of Science JO - CBUJOS PB - Manisa Celal Bayar Üniversitesi WT - DergiPark SN - 1305-130X SP - 755 EP - 759 VL - 13 IS - 3 KW - Class of Maps KW - Convergence of Iteration KW - Data Dependency KW - Fixed Point KW - Iteration N2 - Thispaper concentrates on studying convergence and data dependence of AK iterationfor the class of maps which was introduced by Berinde.  Also, we will support our results with anexample. CR - 1. Berinde, V.; On the convergence of the Ishikawa iteration in the class of quasi contractive operators. Acta Mathematica Universitatis Comenianae, 2004, 73(1), 119-126. CR - 2. Berinde, V.; Iterative approximation of fixed points; Springer: Berlin, Germany, 2007. CR - 3. Schu, J.; Weak and strong convergence to fixed points of asymptotically nonexpansive mappings. Bulletin of the Australian Mathematical Society, 1991, 43(1), 153-159. CR - 4. Ullah, K., and Arshad, M.; On di¤erent results for new three step iteration process in Banach spaces. SpringerPlus 2016, 5(1), 1616. CR - 5. Zamfirescu, T.; Fix point theorems in metric spaces. Archiv der Mathematik 1972, 23(1), 292-298. CR - 6. Berinde, V.; General constructive fixed point theorems for Ciric-type almost contractions in metric spaces. Carpathian Jour-nal of Mathematics. 2008, 24(2), 10-19. CR - 7. Berinde, V., and Pacurar M.; Fixed points and continuity of almost contractions. Fixed Point Theory, 2008, 9(1), 23-34. CR - 8. Karakaya, V., Doğan, K., Gürsoy, F., and Ertürk, M.; Fixed point of a new three-step iteration algorithm under contractivelike operators over normed spaces. Abstract and Applied Analysis, 2013, 2013, 1-9. CR - 9. Khan, A. R., Gürsoy, F., and Karakaya, V.; Jungck-Khan itera-tive scheme and higher convergence rate. International Journal of Computer Mathematics 2016, 93(12), 1029-2105. CR - 10. Gürsoy, F., Karakaya, V., and Rhoades, B. E.; Some conver-gence and stability results for the Kirk multistep and Kirk-SP fixed point iterative algorithms. Abstract and Applied Analysis, 2014, 2014, 1-12. CR - 11. Xu, B., and Noor, M. A.; Fixed-point iterations for asymptoti-cally nonexpansive mappings in Banach spaces. Journal of Mathe-matical Analysis and Applications, 2002, 67(2), 444-453. CR - 12. Weng, X.; Fixed point iteration for local strictly pseudo-contractive mapping. Proceedings of the American Mathematical Society, 1991, 113(3), 727-731. CR - 13. Rhoades, B. E.; Comments on two fixed point iteration met-hods. Journal of Mathematical Analysis and Applications 1976, 56(3), 741-750. CR - 14. Tan, K.K., and Xu, H.; Fixed point iteration processes for asymptotically nonexpansive mappings. Proceedings of the Ameri-can Mathematical Society, 1994, 122(3), 733-739. CR - 15. Şoltuz, Ş. M., and Grosan, T.; Data dependence for Ishikawa iteration when dealing with contractive-like operators. Fixed Point Theory and Applications, 2008, 1, 1-7. CR - 16. Şoltuz, Ş. M.; Data dependence for Mann iteration. Octogon Mathematical Magazine 2001, 9(2), 825-828. CR - 17. Gürsoy, F., Karakaya, V., and Rhoades, B E.; Data dependence results of new multistep and S-iterative schemes for contractive-like operators. Fixed Point Theory and Applications, 2013, 76, 1-12. CR - 18. Şahin, A., and Başarır M.; Convergence and data dependence results of an iteration process in a hyperbolic space. Filomat, 2016, 30(3), 569-582. CR - 19. Khan, A. R., Gürsoy, F., and Kumar V.; Stability and data dependence results for the Jungck-Khan iterative scheme. Turkish Journal of Mathematics 2016, 40, 631-640. UR - https://doi.org/10.18466/cbayarfbe.339352 L1 - https://dergipark.org.tr/tr/download/article-file/345793 ER -