An Inertial Generalized Viscosity Approximation Method for Solving Multiple-Sets Split Feasibility Problems and Common Fixed Point of Strictly Pseudo-Nonspreading Mappings

Hammed Anuoluwapo Abass,Lateef Olakunle Jolaoso

doi:10.3390/axioms10010001

Hammed Anuoluwapo Abass, Lateef Olakunle Jolaoso

Open Access

https://doi.org/10.3390/axioms10010001

Copy DOI

Abstract

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

Highlights

Pseudo-Nonspreading Mappings.The problem of finding a point in the intersection of closed and convex subsets in real Hilbert spaces has appeared severally in diverse areas of mathematics and physical sciences
Is the Split Feasibility Problem (SFP) which was introduced by Censor and Elfving [2] and defined as finding a point in a nonempty closed convex set, whose image under a bounded operator is in another set
Motivated by the works of Wen et al [9] and López et al [6], in this paper, we introduce a general viscosity relaxed projection method with inertial process for solving the MSSFP with the fixed point of strictly pseudo-nonspreading mappings in real Hilbert spaces

Summary

Introduction

López et al [6] introduced a relaxed projection method with a fixed stepsize and proved a weak convergence result for solving the MSSFP. Suantai et al [8] introduced an inertial relaxed projection method with a self-adaptive stepsize for solving the MSSFP. Wen et al [9] introduced a cyclic-simultaneous projection method and proved weak convergence result for solving the MSSFP. Motivated by the works of Wen et al [9] and López et al [6], in this paper, we introduce a general viscosity relaxed projection method with inertial process for solving the MSSFP with the fixed point of strictly pseudo-nonspreading mappings in real Hilbert spaces. Our results improve and complement the results of [6,7,8,9,19,20,21,22,23,24] and many other results in this direction

Preliminaries

Main Results

Numerical Example

Conclusions