We study strong and ∆-convergence of a modified S-type iteration process inspired by Agarwal, O’Regal and Sahu (2007) for uniformly L-Lipschitzian and generalized asymptotically nonexpansive mappings in CAT(0) spaces.

Some variable Krasnonsel’skiı̆-Mann iteration algorithms generate some sequences {xn}, {yn}, and {zn}, respectively, via the formula xn 1 1 − αn xn αnTN · · · T2T1xn, yn 1 1 − βn yn βn ∑N i 1 λiTiyn, zn 1 1 − γn 1 zn γn 1T n 1 zn, where T n TnmodN and the mod function takes values in {1, 2, . . . ,N}, {αn}, {βn}, and {γn} are sequences in 0, 1 , and {T1, T2, . . . , TN} are sequences of nonexpan...

Newton’s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton’s iteration can be done efficiently. We show that the convergence of the modifie...

In this paper, we establish some strong convergence results for Mann and Ishikawa iterative processes in a Banach space setting by employing some general contractive conditions as well as weakening further the conditions on the parameter sequence { n} ⊂ [0, 1]. In addition, in some of our results, we introduce some innovative ideas which make our results distinct from some previous ones. In par...

In this paper, first we use an example to show the efficiency of $M$ iteration process introduced by Ullah and Arshad [4] for approximating fixed points of Suzuki generalized nonexpansive mappings. Then by using $M$ iteration process, we prove some strong and $Delta -$convergence theorems for Suzuki generalized nonexpansive mappings in the setting of $CAT(0)$ Spaces. Our results are the extensi...

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skĭı– Mann iteration built from nonexpansive operators. Our results include two main parts: we first establish global pointwise and ergodic iteration–complexity bounds, and then, under a metric subregularity assumption, we establish local linear convergence for the distance of the iterates to the set of fixed points...