TY - JOUR T1 - The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings AU - Li, Linxin AU - Wu, Dingping PY - 2021 DA - March DO - 10.53006/rna.793940 JF - Results in Nonlinear Analysis JO - RNA PB - Erdal KARAPINAR WT - DergiPark SN - 2636-7556 SP - 47 EP - 56 VL - 4 IS - 1 LA - en AB - Charles[1] proved the convergence of Picard-type iterativefor generalized Φ− accretive non-self maps in a real uniformly smoothBanach space. Based on the theorems of the zeros of strongly Φ− quasi-accretive and fixed points of strongly Φ− hemi-contractions, we extendthe results to Ishikawa iterative and Ishikawa iteration process with er-rors for generalized Φ− hemi-contractive maps . KW - Ishikawa iteration process with errors KW - unique solution KW - strongly Φ−quasi-accretive CR - [1] Charles,Chidume.;Geometric Properties of Banach Spaces and Nonlinear Itera- tions.(2009) CR - [2] Zhiqun Xue,Guiwen Lvand BE Rhoades;the convergence theorems of Ishikawa itera- tive process with errors for hemi-contractive mappings in uniformly smooth Banach spaces,Xue et al. Fixed Point Theory and Applications 2012, 2012:206. CR - [3] Phayap Katchang, Poom Kumam;Strong convergence of the modified Ishikawa itera- tive method for infinitely many nonexpansive mappings in Banach spaces,Computers and Mathematics with Applications 59 (2010) 1473–1483. CR - [4] Abebe R. Tufa and H. Zegeye;Mann and Ishikawa-Type Iterative Schemes for Ap- proximating Fixed Points of Multi-valued Non-Self Mappings,Springer International Publishing 2016. CR - [5] Godwin Amechi Okeke;Convergence analysis of the Picard–Ishikawa hybrid iterative process with applications,African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019. CR - [6] Xu, YG: Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations. J. Math. Anal. Appl. 224, 91-101 (1998). CR - [7] Liu, L.; Ishikawa and Mann iterative process with errors for nonlinear strongly accre- tive mappings in Banach spaces, J. Math. Anal. Appl. 194(1995), no. 1, 114–125. CR - [8] Xu, Y.; Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998), 91–101. CR - [9] Cudia, D. F.; The theory of Banach spaces: Smoothness, Trans. Amer. Math. Soc. 110 (1964), 284–314. CR - [10] Browder, FE: Nonlinear operators and nonlinear equations of evolution in Banach spaces. In: Proc. Of Symposia in Pure Math., Vol. XVIII, Part 2 (1976). UR - https://doi.org/10.53006/rna.793940 L1 - https://dergipark.org.tr/en/download/article-file/1286780 ER -