Taiwanese Journal of Mathematics

GENERALIZED VARIATIONAL INCLUSIONS AND $H$-RESOLVENT EQUATIONS WITH $H$-ACCRETIVE OPERATORS

Rais Ahmad and Qamrul Hasan Ansari

Full-text: Open access

Abstract

In this paper, we consider a more general form of variational inclusions, called generalized variational inclusion (for short, GVI). In connection with GVI, we also consider a generalized resolvent equation with $H$-resolvent operator, called $H$-resolvent equation (for short, $H$-RE). We suggest iterative algorithms to compute the approximate solutions of GVI and $H$-RE. The existence of a unique solution of GVI and $H$-RE and convergence of iterative sequences generated by the proposed algorithms are also studied. Several special cases are also discussed.

Article information

Source
Taiwanese J. Math., Volume 11, Number 3 (2007), 703-716.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404753

Digital Object Identifier
doi:10.11650/twjm/1500404753

Mathematical Reviews number (MathSciNet)
MR2340159

Zentralblatt MATH identifier
1138.49008

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 47H06: Accretive operators, dissipative operators, etc. 49J53: Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]

Keywords
generalized variational inclusions $H$-resolvent equations $H$-resolvent operators $H$-accretive mappings iterative algorithms convergence results

Citation

Ahmad, Rais; Ansari, Qamrul Hasan. GENERALIZED VARIATIONAL INCLUSIONS AND $H$-RESOLVENT EQUATIONS WITH $H$-ACCRETIVE OPERATORS. Taiwanese J. Math. 11 (2007), no. 3, 703--716. doi:10.11650/twjm/1500404753. https://projecteuclid.org/euclid.twjm/1500404753


Export citation