Abstract
The purpose of this paper is to prove some fixed point results dealing with a system of nonlinear equations defined in an angelic Hausdorff locally convex space
(
X
,
{
|
⋅
|
p
}
p
∈
Λ
)
(X,\{\lvert\,{\cdot}\,\rvert_{p}\}_{p\in\Lambda})
having the 𝜏-Krein–Šmulian property, where 𝜏 is a weaker Hausdorff locally convex topology of 𝑋.
The method applied in our study is connected with a family
Φ
Λ
τ
\Phi_{\Lambda}^{\tau}
-MNC of measures of weak noncompactness and with the concept of 𝜏-sequential continuity.
As a special case, we discuss the existence of solutions for a
2
×
2
2\times 2
block operator matrix with nonlinear inputs.
Furthermore, we give an illustrative example for a system of nonlinear integral equations in the space
C
(
R
+
)
×
C
(
R
+
)
C(\mathbb{R}^{+})\times C(\mathbb{R}^{+})
to verify the effectiveness and applicability of our main result.
Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces
