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Volume 7, Issue 2
Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations

H. El Bazi & A. Sadrati

DOI: 10.12150/jnma.2025.720

J. Nonl. Mod. Anal., 7 (2025), pp. 720-738.

Published online: 2025-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this work, we establish a new existence and uniqueness of vector fixed point for a class of sum-type vector operators with some mixed monotone property in partially ordered product Banach spaces. The technique used is Thompson’s part metric, and our goal is to extend and improve existing works in the scalar case vector case. As an application, we study the existence and uniqueness of solutions for systems of nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

  • Keywords

Mixed monotone vector operators, Meir-Keeler type, systems of nonlinear elastic beams equations, Thompson metric, $ε$-chainable metric space.

  • AMS Subject Headings

47H10, 45G15, 35G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-720, author = {Bazi , H. El and Sadrati , A.}, title = {Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {2}, pages = {720--738}, abstract = {

In this work, we establish a new existence and uniqueness of vector fixed point for a class of sum-type vector operators with some mixed monotone property in partially ordered product Banach spaces. The technique used is Thompson’s part metric, and our goal is to extend and improve existing works in the scalar case vector case. As an application, we study the existence and uniqueness of solutions for systems of nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.720}, url = {http://global-sci.org/intro/article_detail/jnma/24024.html} }
TY - JOUR T1 - Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations AU - Bazi , H. El AU - Sadrati , A. JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 720 EP - 738 PY - 2025 DA - 2025/04 SN - 7 DO - http://doi.org/10.12150/jnma.2025.720 UR - https://global-sci.org/intro/article_detail/jnma/24024.html KW - Mixed monotone vector operators, Meir-Keeler type, systems of nonlinear elastic beams equations, Thompson metric, $ε$-chainable metric space. AB -

In this work, we establish a new existence and uniqueness of vector fixed point for a class of sum-type vector operators with some mixed monotone property in partially ordered product Banach spaces. The technique used is Thompson’s part metric, and our goal is to extend and improve existing works in the scalar case vector case. As an application, we study the existence and uniqueness of solutions for systems of nonlinear singular fourth-order elastic beam equations with nonlinear boundary conditions.

Bazi , H. El and Sadrati , A.. (2025). Vector Fixed Point Theorem with Application to Systems of Nonlinear Elastic Beams Equations. Journal of Nonlinear Modeling and Analysis. 7 (2). 720-738. doi:10.12150/jnma.2025.720
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