Economic equilibrium problems in reflexive Banach spaces

2006 ◽  
Vol 65 (10) ◽  
pp. 1925-1954 ◽  
Author(s):  
Zdzisław Naniewicz
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Economic Equilibrium ◽  
Reflexive Banach Spaces

scholarly journals Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
N. K. Mahato ◽  
C. Nahak
Keyword(s):  
Equilibrium Problem ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
Generalized Monotonicity ◽  
Reflexive Banach Spaces ◽  
Strong Pseudomonotonicity ◽  
Pseudomonotone Maps ◽  
Pseudomonotone Mappings

We introduce the notion of relaxed (ρ-θ)-η-invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed (ρ-θ)-η-invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of (ρ-θ)-pseudomonotonicity for bifunctions, and we consider some examples to show that (ρ-θ)-pseudomonotonicity generalizes both monotonicity and strong pseudomonotonicity. The existence of solution for equilibrium problem with (ρ-θ)-pseudomonotone mappings in reflexive Banach spaces are demonstrated by using the KKM technique.

scholarly journals A monotone Bregan projection algorithm for fixed point and equilibrium problems in a reflexive Banach space

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1487-1497
Author(s):  
Sun Cho
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Reflexive Banach Space ◽  
Fixed Point Problems ◽  
Projection Algorithm ◽  
Reflexive Banach Spaces

In this paper, a monotone Bregan projection algorithm is investigated for solving equilibrium problems and common fixed point problems of a family of closed multi-valued Bregman quasi-strict pseudocontractions. Strong convergence is guaranteed in the framework of reflexive Banach spaces.

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