<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this paper, we introduce and study a new class of nonlinear vari- ational inclusion problems with Lipschitz k-subaccretive type mappings in real reflexive Banach spaces. The existence and uniqueness of such solutions are proved and the convergence and stability of Noor iterative sequences with errors are also discussed. Furthermore, general conver- gence rate estimates are given in our results, which essentially improve and extend the corresponding results in Chang[1, 2], Ding[3], Gu[5, 6, 7], Hassouni andMoudafi[8], Kazmi[9], Noor[11, 12], Siddiqi and Ansari[13], Siddiqi, Ansari and Kazmi[14] and Zeng[16].</p></abstract>

In this paper, we introduce and study a new class of nonlinear vari- ational inclusion problems with Lipschitz k-subaccretive type mappings in real reflexive Banach spaces. The existence and uniqueness of such solutions are proved and the convergence and stability of Noor iterative sequences with errors are also discussed. Furthermore, general conver- gence rate estimates are given in our results, which essentially improve and extend the corresponding results in Chang[1, 2], Ding[3], Gu[5, 6, 7], Hassouni andMoudafi[8], Kazmi[9], Noor[11, 12], Siddiqi and Ansari[13], Siddiqi, Ansari and Kazmi[14] and Zeng[16].

Noor Iterative Approximation for Solutions to Variational Inclusions with k-Subaccretive Type Mappings in Reflexive Banach Spaces

Department of Mathematics, BoHai University, Jinzhou, Liaoning, 121013, China

Dalian City No.37 Middle School, Dalian, Liaoning, 116011, China

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

In this paper, we introduce and study a new class of nonlinear vari- ational inclusion problems with Lipschitz k-subaccretive type mappings in real reflexive...

Noor Iterative Approximation for Solutions to Variational Inclusions with k-Subaccretive Type Mappings in Reflexive Banach Spaces

Published Online: May 17, 2013

Page range: 505 - 517

DOI: https://doi.org/10.2478/v10309-012-0034-3

Keywords
variational inclusion, k-subaccretive operator, T-stability, convergence rate estimate, Noor three-step iterative sequences with errors

This content is open access.

Noor Iterative Approximation for Solutions to Variational Inclusions with k-Subaccretive Type Mappings in Reflexive Banach Spaces

Published Online: May 17, 2013

Page range: 505 - 517

DOI: https://doi.org/10.2478/v10309-012-0034-3

Keywordsvariational inclusion, k-subaccretive operator, T-stability, convergence rate estimate, Noor three-step iterative sequences with errors

This content is open access.

Keywords
variational inclusion, k-subaccretive operator, T-stability, convergence rate estimate, Noor three-step iterative sequences with errors