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Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces

  • Fatima Bahidi , Bilel Krichen ORCID logo EMAIL logo and Bilel Mefteh
Published/Copyright: January 4, 2022
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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 ) 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 -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 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 + ) to verify the effectiveness and applicability of our main result.

MSC 2010: 47H10; 47H08; 45G15

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Received: 2020-09-07
Accepted: 2021-01-28
Published Online: 2022-01-04
Published in Print: 2022-04-01

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