A New Generalized Resolvent and Application in Banach Spaces
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.
Abstract
In this paper, we introduce a new generalized resolvent in a Banach space and discuss its some properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved.
참고문헌 (8)
- D.Pascali, ", editura. academiae" (1978), Romania
- Habtu Zegeye, "Strong convergence theorems for monotone mappings and relatively weak nonexpansive mappings", Nonl. Anal, 70, pp.2707~2716 (2009)
- I. Cioranescu, "Geometry of Banach spaces, Duality Mapping and Nonlinear Problems" (1990), Klumer. Academic. publishers
- Jinlu Li, "On the existence of solutions of variational inequalities in Banach spaces", J. Math. Anal. Appl, 295, pp.115~126 (2008)
- S. Reich, "Constructive techniques for accretive and monotone operators", Appl. Nonl. Anal, pp.335~345 (1979)
- Takanori Ibaraki, "A new projection and convergence theorems for the projections in Banach spaces", J. Appr. Theory, 149, pp.1~14 (2007)
- Ya. Alber, "Theory and Applications of Nonlinear Operators of Monotonic and Accretive Type" (1996), Marcel. Dekker
- Y. Su, "Monotone CQ iteration processes for nonexpansive semigroups and maximal monotone operators", Nonl. Anal, 68, pp.3657~3664 (2008)