en عمومى General پژوهشي Research paper <p style="margin: 0px; text-indent: 0px; text-align: justify;">Suppose C is any nonempty subset of a Banach space X. A mapping T : C &rarr; C is said to satisfy condition (B_{&gamma;,&micro;}) if there exists &gamma; &isin; [0, 1] and &micro; &isin; [0, 1 /2 ] with 2&micro; &le; &gamma; such that for each two elements x, y &isin; C,</p> <p style="margin: 0px; text-indent: 0px; text-align: center;">&gamma;||x - T x|| &le; ||x - y|| + &micro;||y - T y||</p> <p style="margin: 0px; text-indent: 0px; text-align: center;">implies ||T x - T y|| &le; (1 - &gamma;)||x - y|| + &micro;(||x - T y|| + ||y - T x||).</p> <p style="margin: 0px; text-indent: 0px; text-align: justify;">In this research, we suggest some convergence results for these mappings under a up-to-date iterative process in a Banach space setting. Our results are new and improve some known results of the literature.</p> Condition $(B_{gamma,mu})$, Condition (I), Convergence result, K* iteration, Banach space. 135 148 http://ijmsi.ir/browse.php?a_code=A-10-5212-1&slc_lang=en&sid=1 Kifayat Ullah kifayatmath@yahoo.com 100319475328460010680 100319475328460010680 Yes Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat-28420, Khyber Pakhtunkhwa, Pakistan Mujahid Abbas abbas.mujahid@gmail.com 100319475328460010681 100319475328460010681 No Department of Mathematics, Government College University, Lahore 54000, Pakistan Junaid Ahmad ahmadjunaid436@gmail.com 100319475328460010682 100319475328460010682 No Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad - 44000, Pakistan Fayyaz Ahmad fayyaz.rana83@gmail.com 100319475328460010683 100319475328460010683 No Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat-28420, Khyber Pakhtunkhwa, Pakistan