Different approaches to the existence of projected solutions in Banach spaces

M. Bianchi; J. Cotrina; Y. García; R. Pini

doi:10.1080/02331934.2025.2553195

Different approaches to the existence of projected solutions in Banach spaces

M. Bianchi
, J. Cotrina
, Y. García
, R. Pini

Producción científica: Contribución a una revista › Artículo de revista › revisión exhaustiva

Resumen

Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.

Idioma original	Inglés
Publicación	Optimization
DOI	https://doi.org/10.1080/02331934.2025.2553195
Estado	Publicación electrónica previa a su impresión - 2025

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© 2025 Informa UK Limited, trading as Taylor & Francis Group.

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10.1080/02331934.2025.2553195

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title = "Different approaches to the existence of projected solutions in Banach spaces",

abstract = "Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.",

keywords = "fixed point theorem, Generalized equilibrium problem, projection map, vector variational inequalities",

author = "M. Bianchi and J. Cotrina and Y. Garc{\'i}a and R. Pini",

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TY - JOUR

T1 - Different approaches to the existence of projected solutions in Banach spaces

AU - Bianchi, M.

AU - Cotrina, J.

AU - García, Y.

AU - Pini, R.

PY - 2025

Y1 - 2025

N2 - Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.

AB - Quasi-equilibrium problems generalize equilibrium problems, as introduced in the framework of Blum and Oettli. This study focuses on quasi-equilibrium problems in which the constraint map is not a self-map. We present various reformulations that establish existence results for projected solutions in Banach spaces. Furthermore, we apply these findings to quasi-variational inequalities and quasi-optimization problems.

KW - fixed point theorem

KW - Generalized equilibrium problem

KW - projection map

KW - vector variational inequalities

UR - https://www.scopus.com/pages/publications/105015325947

UR - https://www.mendeley.com/catalogue/fd74a187-3219-33d0-92db-52f62f168e67/

U2 - 10.1080/02331934.2025.2553195

DO - 10.1080/02331934.2025.2553195

M3 - Artículo de revista

AN - SCOPUS:105015325947

SN - 0233-1934

JO - Optimization

JF - Optimization

ER -

Different approaches to the existence of projected solutions in Banach spaces

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