Abstract
AbstractWe introduce a new iterative method for finding a common element of the set of fixed points of pseudo-contractive mapping, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. We provide some results about strongly and weakly convergent of the iterative scheme sequence to a point $p\in \varOmega $
p
∈
Ω
which is the unique solution of a variational inequality, where Ω is an intersection of set as given by ${\varOmega }=F(S)\cap (A+B)^{-1}(0) \cap N^{-1}(0)\cap \operatorname{GEP}(F,M)\neq \emptyset $
Ω
=
F
(
S
)
∩
(
A
+
B
)
−
1
(
0
)
∩
N
−
1
(
0
)
∩
GEP
(
F
,
M
)
≠
∅
. This gives us a common solution. Also, We show that our results extend some published recent results in this field. Finally, we provide an example to illustrate our main result.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference41 articles.
1. Ceng, L.C., Petrusel, A., Yao, J.C.: Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudo-contractive mappings. Appl. Math. Comput. 209, 162–176 (2009)
2. Ishikawa, S.: Fixed points by a new iteration method. Proc. Am. Math. Soc. 44(1), 147–150 (1974)
3. Kamimura, S., Takahashi, W.: Approximating solutions of maximal monotone operators in Hilbert spaces. J. Approx. Theory 106, 226–240 (2000)
4. Wang, Y.H., Rezapour, S., Zakeri, S.H.: Strong convergence theorems for Bregman relatively nonexpansive mappings and continuous monotone mapping. J. Nonlinear Convex Anal. 20(3), 551–564 (2019)
5. Zhang, Q.B., Cheng, C.Z.: Strong convergence theorem for a family of Lipschitz pseudo-contractive mappings in a Hilbert space. Math. Comput. Model. 48, 480–485 (2008)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献