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A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces

Jolaoso Lateef Olakunle, Taiwo Adeolu, Alakoya Timilehin Opeyemi, Mewomo Oluwatosin Temitope

Demonstratio Mathematica

2019

Vol. 52, nr 1

183--203

We consider a new subgradient extragradient iterative algorithm with inertial extrapolation for approximating a common solution of variational inequality problems and fixed point problems of a multivalued demicontractive mapping in a real Hilbert space. We established a strong convergence theorem for our proposed algorithm under some suitable conditions and without prior knowledge of the Lipschitz constant of the underlying operator. We present numerical examples to show that our proposed algorithm performs better than some recent existing algorithms in the literature.

A unified algorithm for solving split generalized mixed equilibrium problem, and for finding fixed point of nonspreading mapping in Hilbert spaces

Jolaoso L. O., Oyewole K. O., Okeke C. C., Mewomo O. T.

Demonstratio Mathematica

2018

Vol. 51, nr 1

211--232

The purpose of this paper is to study a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. We introduce a new iterative algorithm and prove its strong convergence for approximating a common solution of a split generalized mixed equilibrium problem and a fixed point problem for nonspreading mappings in real Hilbert spaces. Our algorithm is developed by combining a modified accelerated Mann algorithm and a viscosity approximation method to obtain a new faster iterative algorithm for finding a common solution of these problems in real Hilbert spaces. Also, our algorithm does not require any prior knowledge of the bounded linear operator norm. We further give a numerical example to show the efficiency and consistency of our algorithm. Our result improves and compliments many recent results previously obtained in this direction in the literature.