Abstract
In this paper, we introduce and study generalized variational inclusions and generalized resolvent equations in real Banach spaces. It is established that generalized variational inclusion problems in uniformly smooth Banach spaces are equivalent to fixed-point problems. We also establish a relationship between generalized variational inclusions and generalized resolvent equations. By using Nadler's fixed-point theorem and resolvent operator technique for m-accretive mappings in real Banach spaces, we propose an iterative algorithm for computing the approximate solutions of generalized variational inclusions. The iterative algorithms for finding the approximate solutions of generalized resolvent equations are also proposed. The convergence of approximate solutions of generalized variational inclusions and generalized resolvent equations obtained by the proposed iterative algorithms is also studied. Our results are new and represent a significant improvement of previously known results. Some special cases are also discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 1825-1835 |
| Number of pages | 11 |
| Journal | Computers and Mathematics with Applications |
| Volume | 49 |
| Issue number | 11-12 |
| DOIs | |
| State | Published - Jun 2005 |
Bibliographical note
Funding Information:The research work of the first author was done during hm vmlt to the Abdus Salam ICTP, Trieste, Italy While the second author is grateful to the Department of MathematmM Scmnces, King Fahd Umvermty of Petroleum and Minerals, Dhahran, Saudi Arabla for provldmg excellent research facihtms to carry out hm part of research work *On leave from the Department of Mathematles, Ahgarh Mushm Umverslty, Ahgarh, India
Keywords
- Convergence results
- Generalized resolvent equations
- Generalized variational inclusions
- Iterative algorithms
- Resolvent operators
- m-accretive mappings
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics