Geodesic
$H(.,.)-\eta$-cocoercive operators and variational-like inclusions in Banach spaces
Ahmad, Rais1 ; Dilshad, Mohammad1
1 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 334-344.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we define $H(.,.)-\eta$-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent operator. We prove the Lipschitz continuity of the resolvent operator associated with $H(.,.)-\eta$-cocoercive operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved. Some examples are given.
DOI : 10.22436/jnsa.005.05.03
Classification : 47H19, 49J40
Keywords: \(H(., .)-\eta\)-cocoercive, Algorithm, Inclusion, Banach spaces, Lipschitz continuity.

Ahmad, Rais 1 ; Dilshad, Mohammad 1

1 Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India 
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Ahmad, Rais; Dilshad, Mohammad. \(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 334-344. doi : 10.22436/jnsa.005.05.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.05.03/

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