Geodesic
Extragradient method for approximating a common solution for a fixed point and variational inequality problems in Hilbert space
Novi Sad Journal of Mathematics, Tome 52 (2022) no. 2.

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In this paper, we introduce an extragradient method to approximate a common solution of variational inequality problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequence generated by the iterative algorithm converges strongly to a common solution of a variational inequality problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in the literature. Some applications of main results are also provided.
Publié le :
DOI : 10.30755/NSJOM.09578
Classification : 47H09, 47H10, 90H10
Keywords: Extragradient method, Fixed points, variational inequality problem, asymptotically nonexpansive mapping, $ \alpha $-inverse strongly monotone mapping 
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     title = {Extragradient method for approximating a common solution  for a fixed point and variational inequality problems in {Hilbert} space},
     journal = {Novi Sad Journal of Mathematics},
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Santosh Kumar; Richard Osward; Mengistu Goa Sangago. Extragradient method for approximating a common solution  for a fixed point and variational inequality problems in Hilbert space. Novi Sad Journal of Mathematics, Tome 52 (2022) no. 2. doi : 10.30755/NSJOM.09578. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.09578/

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