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Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces.
- Source :
-
Georgian Mathematical Journal . Apr2022, Vol. 29 Issue 2, p179-192. 14p. - Publication Year :
- 2022
-
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 휏-Krein–Šmulian property, where 휏 is a weaker Hausdorff locally convex topology of 푋. 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 휏-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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1072947X
- Volume :
- 29
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Georgian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 155973857
- Full Text :
- https://doi.org/10.1515/gmj-2021-2127