TY - JOUR T1 - A generalized nonlinear iterative algorithm for the explicit midpoint rule of nonexpansive semigroup AU - Sahebi, Hamid Reza AU - Azhını, Mahdi AU - Cheraghi, Masume PY - 2020 DA - June Y2 - 2019 DO - 10.31801/cfsuasmas.484452 JF - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JO - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. PB - Ankara University WT - DergiPark SN - 1303-5991 SP - 613 EP - 628 VL - 69 IS - 1 LA - en AB - In this paper, we introduce a new iterative midpoint rule for finding a solution ofxed point problem for a nonexpansive semigroup in real Hilbert spaces. We establisha strong convergence theorem for the sequences generated by our proposed iterativescheme. Furthermore, we provide application to Fredholm integral equations. Anumerical example is presented to illustrate the convergence result. Our resultsimprove and extend the corresponding results in the literature. 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CR - Xu, H.K., Alghamdi, M.A. and Shahzad, N., The viscosity technique for the implicit mid point rule of nonexpansive mappings in Hilbert spaces, Fixed point Theory Appl., 41 (2015), 12 pages. UR - https://doi.org/10.31801/cfsuasmas.484452 L1 - https://dergipark.org.tr/en/download/article-file/942886 ER -