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An extragradient inertial algorithm for solving split fixed-point problems of demicontractive mappings, with equilibrium and variational inequality problems

Okeke Chibueze C., Ugwunnadi Godwin C., Jolaoso Lateef O.

Demonstratio Mathematica

2022

Vol. 55, nr 1

506--527

The purpose of this article is to study and analyse a new extragradient-type algorithm with an inertial extrapolation step for solving split fixed-point problems for demicontractive mapping, equilibrium problem, and pseudomonotone variational inequality problem in real Hilbert spaces. One of the advantages of the proposed algorithm is that a strong convergence result is achieved without a prior estimate of the Lipschitz constant of the cost operator, which is very difficult to find. In addition, the stepsize is generated at each iteration by some simple computations, which allows it to be easily implemented without the prior knowledge of the Lipschitz constant of the cost operator. Some numerical experiments are reported to show the performance and behaviour of the sequence generated by our algorithm. The obtained results in this article extend and improve many related recent results in this direction in the literature.

General iterative method for solving fixed point problems involving a finite family of demicontractive mappings in Banach spaces

Sow Thierno M. M.

Commentationes Mathematicae

2019

Vol. 59, No. 1/2

63--80

The purpose of this paper is to study the general iterative method for demicontractive mappings in Banach spaces. The method gives us a strong convergence iteration for a finite family of demicontractive mappings and also permits us to solve variational inequality problems involving accretive operators without any compactness condition. Finally, we provide some applications, and an illustration of the proposed method is given in l4 spaces. Our results improve many recent results using the general iterative method for finding the fixed points of nonlinear operators.