General equilibrium and fixed point theory: A partial survey

General Equilibrium and Fixed Point Theory: a Partial Survey

Focusing mainly on equilibrium existence results, this paper emphasizes the role of fixed point theorems in the development of general equilibrium theory, as well for its standard definition as for some of its extensions. Mathematics Subject Classification: Primary 47H10, 47H11, 47N10, 49J53, 54H25, 58C30

A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

and Applied Analysis 3 literature. For some works related to the equilibrium problem, fixed point problems, and the variational inequality problem, please see 1–57 and the references therein. However, we note that all constructed algorithms in 7, 9–13, 16, 57 do not work to find the minimum-norm solution of the corresponding fixed point problems and the equilibrium problems. Very recently, Yao ...

A Short Survey of the Development of Fixed Point Theory

In this survey paper, we collected the developmental history of fixed point theory. Some important results from beginning up to now are incorporated in this paper. Full text

On fixed point theory in partial metric spaces

In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Moreover, the well-posedness of the fixed point p...

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems