A Simultaneous Iteration Algorithm for Solving Extended Split Equality Fixed Point Problem

Abstract

We study a kind of split equality fixed point problem which is an extension of split equality problem. We propose a kind of simultaneous iterative algorithm with a way of selecting the step length which does not need any a priori information about the operator norms and prove that the sequences generated by the iterative method converge weakly to the solution of this problem. Some numerical results are shown to confirm the feasibility and efficiency of the proposed methods.

Mixed Simultaneous Iterative Algorithms for the Extended Multiple‐Set Split Equality Common Fixed‐Point Problem with Lipschitz Quasi‐Pseudocontractive Operators

“…In particular, if = = 1, then MSECFP (9) reduces to the split equality common fixed-point problem (SECFP) (5). They proposed the following iterative algorithm: Recently, Li et al [22] studied the extended split equality common fixed-point problem (ESECFP) which is to find…”

A Special Mutation Operator in the Genetic Algorithm for Fixed Point Problems

“…The relationship between the genetic algorithm and the fixed points is a two-way relationship. In this sense, in some studies, fixed point properties have been used to improve the performance of genetic algorithms [13][14][15][16][17][18], and in some studies, updated models of genetic algorithms have been used to solve fixed point problems [19][20][21][22].…”

An alternating iteration algorithm for solving the split equality fixed point problem with L-Lipschitz and quasi-pseudo-contractive mappings

“…Under suitable conditions, he proved the weak convergence of the sequence {(x n , y n )} to a solution of (1.6) in Hilbert spaces. About the study of algorithms and theories for solving (1.6), the reader can also see [14,17] and the references therein.…”