Abstract
AbstractLet C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$
T
:
C
→
C
B
(
H
)
be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$
T
:
C
→
P
r
o
x
(
H
)
is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.
Publisher
Springer Science and Business Media LLC
Reference32 articles.
1. Abbas, M.; Cho, Y.J.: Fixed point results for multi-valued non-expansive mappings on an unbounded set. Analele Stiintifice ale Universitatii Ovidius Constanta 18(2), 5–14 (2010)
2. Alber, Ya.: Metric and generalized projection operators in Banach spaces: properties and applications. In: Kartsatos, A.G. (ed.) Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. Lecture Notes in Pure and Appl. Math., vol. 178, pp. 15–50. Dekker, New York (1996)
3. Beg, I.; Abbas, M.: Fixed-point theorem for weakly inward multi-valued maps on a convex metric space. Demonstr. Math. 39(1), 149–160 (2006)
4. Benavides, T.D.; Ramírez, P.L.: Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions. J. Math. Anal. Appl. 291(1), 100–108 (2004)
5. Chidume, C. E., Chidume, C. O., Djitte, N., Minjibir, M. S.: Convergence theorems for fixed points of multivalued strictly pseudocontractive mappings in Hilbert spaces. In Abstract and Applied Analysis, Hindawi Publishing Corporation, Vol. 2013 (2013)