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

Author:

Jolaoso Lateef Olakunle1,Taiwo Adeolu2,Alakoya Timilehin Opeyemi3,Mewomo Oluwatosin Temitope4

Affiliation:

1. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa ; E-mail: 216074984@stu.ukzn.ac.za

2. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa ;

3. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa ; E-mail: 218086823@stu.ukzn.ac.za

4. School of Mathematics, Statistics and Computer Science , University of KwaZulu-Natal , Durban , South Africa

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference53 articles.

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2. [2] Aremu K. O., Izuchukwu C., Ugwunnadi G. C., Mewomo O. T., On the proximal point algorithm and demimetric mappings in CAT(0) spaces, Demonstr. Math., 2018, 51, 277-294

3. [3] Okeke C. C., Mewomo O. T., On split equilibriumproblem, variational inequality problem and fixed point problem for multivalued mappings, Ann. Acad. Rom. Sci. Ser. Math. Appl., 2017, 9(2), 223-248

4. [4] Okeke C. C., Bello A. U., Izuchukwu C., Mewomo O. T., Split equality for monotone inclusion problem and fixed point problem in real Banach spaces, Aust. J. Math. Anal. Appl., 2017, 14(2), 1-20

5. [5] Izuchukwu C., Aremu K. O., Mebawondu A. A., Mewomo O. T., A viscosity iterative technique for equilibriumand fixed point problems in a Hadamard space, Appl. Gen. Topol., 2019, doi:10.4995/agt.2019.10635

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