Hybrid projection algorithm concerning split equality fixed point problem for quasi-pseudo-contractive mappings with application to optimization problem

Abstract

The purpose of this paper is by using the shrinking projection method to study the split equality fixed point problem for a class of quasi-pseudo-contractive mappings in the setting of Hilbert spaces. Under suitable conditions, some strong convergence theorems are obtained. As applications, we utilize the results presented in the paper to study the existence problem of solutions to the split equality variational inequality problem and the split equality convex minimization problem. The results presented in our paper extend and improve some recent results. c 2016 all rights reserved.Keywords: Split equality fixed point problem, quasi-pseudo-contractive mapping, hybrid projection algorithm, strong convergence theorem. 2010 MSC: 47J20, 47H10, 49J25.

The strong convergence theorems for the split equality fixed point problems in Hilbert spaces

“…Remark 3.2. Since a quasi-pseudo-contractive mapping is a quasi-aymptotically pseudo-contractive mapping, the Theorem 3.1 extends the main results in [17] and [19] from quasi-pseudo-contractive mappings to quasi-aymptotically pseudo-contractive mappings.…”

“…In 2016, Tang et al [19] used the following hybrid projection algorithm to solve split equality fixed point problem (SEF P P ) for L-Lipschitzian and quasi-pseudo-contractive mappings in Hilbert spaces and proved its strong convergence theorem without assumption of semi-compactness on mappings:…”