Existence and well-posedness for excess demand equilibrium problems

Lam Quoc Anh; Pham Thanh Duoc; Tran Quoc Duy

doi:10.3934/naco.2021043

Article Contents

2023, Volume 13, Issue 1: 45-52. Doi: 10.3934/naco.2021043

This issue Previous Article A novel differential evolution algorithm for economic power dispatch problem Next Article Modified Dai-Yuan iterative scheme for nonlinear systems and its application

Existence and well-posedness for excess demand equilibrium problems

1.
Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam
2.
University of Science, Ho Chi Minh City, Vietnam, Vietnam National University, Ho Chi Minh City, Vietnam
3.
Department of Mathematics, Vo Truong Toan University, Hau Giang, Vietnam
4.
Department of Mathematics, FPT University, Can Tho, Vietnam

^* Corresponding author: Tran Quoc Duy
^* Corresponding author: Tran Quoc Duy

Received: February 2021

Revised: September 2021

Early access: October 2021

Published: March 2023

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Abstract

In this paper, we study excess demand equilibrium problems in Euclidean spaces. Applying the Glicksberg's fixed point theorem, sufficient conditions for the existence of solutions for the reference problems are established. We introduce a concept of well-posedness, say Levitin–Polyak well-posedness in the sense of Painlevé–Kuratowski, and investigate sufficient conditions for such kind of well-posedness.

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Mathematics Subject Classification: Primary: 49J40, 46N10; Secondary: 90C29.

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