Abstract
In this paper, we propose an iterative algorithm for finding solution of split feasibility problem involving a λ−strictly pseudo-nonspreading map and asymptotically nonexpansive semigroups in two real Hilbert spaces. We prove weak and strong convergence theorems using the sequence obtained from the proposed algorithm. Finally, we applied our result to solve a monotone inclusion problem and present a numerical example to support our result.
Highlights
The split feasibility problem (SFP) in finite dimensional Hilbert spaces was first introduced by Censor and Elfving [1] for modelling inverse problems which arise from phase retrievals and in medical image reconstruction
Motivated by the recent research going on in the direction of split common fixed point problems, it is our purpose in this paper to construct an iterative algorithm for approximating solution of split feasibility problem involving a strictly pseudo-nonspreading map and asymptotically nonexpansive semigroup in real Hilbert spaces
In this work, we proved weak and strong convergence Theorems for solving split feasibility problem involving a strictly pseudo-nonspreading mapping and asymptotically nonexpansive semigroup in infinite dimensional real Hilbert spaces
Summary
The split feasibility problem (SFP) in finite dimensional Hilbert spaces was first introduced by Censor and Elfving [1] for modelling inverse problems which arise from phase retrievals and in medical image reconstruction. Inspired by definition (3.1) of [8] and the definition of asymptotically strict pseudocontractive mappings given by Qihuo [9], Quan and Chang [10] introduced and studied a class of maps called k− strictly asymptotically pseudo- nonspreading maps in a real Hilbert space They obtained some convergence theorems for solving SCFPP involving the class of k− strictly asymptotically pseudo- nonspreading mappings. Motivated by the recent research going on in the direction of split common fixed point problems, it is our purpose in this paper to construct an iterative algorithm for approximating solution of split feasibility problem involving a strictly pseudo-nonspreading map and asymptotically nonexpansive semigroup in real Hilbert spaces. The result obtained improve on the results of Chang et al [10], complements the results of; Cholamjiak and Shehu [11], Ezeora and Ogbonna [13], Moudafi [6] and many others
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