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
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