Viscosity S-iteration method with inertial technique and self-adaptive step size for split variational inclusion, equilibrium and fixed point problems

2022 ◽  
Vol 41 (1) ◽  
Author(s):  
T. O. Alakoya ◽  
O. T. Mewomo
Keyword(s):  
Fixed Point ◽  
Iteration Method ◽  
Fixed Point Problems ◽  
Variational Inclusion ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Inertial Technique ◽  
Self Adaptive

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

Axioms ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 1
Author(s):  
Hammed Anuoluwapo Abass ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Feasibility Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Step Size ◽  
Adaptive Step Size ◽  
Adaptive Step ◽  
Split Feasibility ◽  
Self Adaptive

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.

scholarly journals A Relaxed Self-Adaptive Projection Algorithm for Solving the Multiple-Sets Split Equality Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Haitao Che ◽  
Haibin Chen
Keyword(s):  
Fixed Point ◽  
Equation System ◽  
Projection Algorithm ◽  
Step Size ◽  
Split Equality Problem ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Equality Problem ◽  
Adaptive Step ◽  
Self Adaptive

In this article, we introduce a relaxed self-adaptive projection algorithm for solving the multiple-sets split equality problem. Firstly, we transfer the original problem to the constrained multiple-sets split equality problem and a fixed point equation system is established. Then, we show the equivalence of the constrained multiple-sets split equality problem and the fixed point equation system. Secondly, we present a relaxed self-adaptive projection algorithm for the fixed point equation system. The advantage of the self-adaptive step size is that it could be obtained directly from the iterative procedure. Furthermore, we prove the convergence of the proposed algorithm. Finally, several numerical results are shown to confirm the feasibility and efficiency of the proposed algorithm.

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