TY - JOUR
T1 - An inertial generalized viscosity approximation method for solving multiple-sets split feasibility problems and common fixed point of strictly pseudo-nonspreading mappings
AU - Abass, Hammed Anuoluwapo
AU - Jolaoso, Lateef Olakunle
N1 - Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2021/3
Y1 - 2021/3
N2 - 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.
AB - 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.
KW - Fixed point problem
KW - Multiple-sets split feasibility problem
KW - Nonexpan-sive mappings
KW - Strictly pseudocontractive mappings
KW - Viscossity iterative scheme
UR - http://www.scopus.com/inward/record.url?scp=85099287177&partnerID=8YFLogxK
U2 - 10.3390/axioms10010001
DO - 10.3390/axioms10010001
M3 - Article
AN - SCOPUS:85099287177
SN - 2075-1680
VL - 10
SP - 1
EP - 18
JO - Axioms
JF - Axioms
IS - 1
M1 - 1
ER -