and Applied Analysis 3 Remark 1.2. i Since 0 αn βn 1, n 1 and ∑∞ n 1 αnβn ∞, the iterative sequence 1.6 could not be reduced to a Mann iterative sequence 1.4 . Therefore, the iterative sequence 1.6 has some particular cases. ii The iterative sequence 1.6 is usually called the Ishikawa iterative sequence. iii Chidume andMutangadura 17 gave an example to show that the Mann iterative sequence fail...

We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. As ap...

Abstract In this paper, we present Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems k -strictly pseudocontractive nonself-mappings. We establish that the weak convergence of proposed accelerated iterative with terms involves a step size which does not require any prior knowledge operator norm under several suitable cond...