A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces

Acta Mathematicae Applicatae Sinica, English Series Vol. 19, No. 3 (2003) 425–430 A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in H-spaces Ji-cheng Hou Department of Mathematics, Shantou University, Shantou 515063, China (E-mail: hjc@ytu.edu.cn) Correspondence address: Department of Mathematics and Information Science, Yantai University, Yantai 264005, China Abstract In this note we first prove a fixed point theorem in H-spaces which unities and extends the corre- sponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4]. Keywords H-space, fixed points, abstract economy, non-compact domain, Nash equilibria, compactly open lower sections 2000 MR Subject Classification 47H10, 91A10, 91A13 1 Introduction Recently, in [9] Huang extended the Fan-Browder fixed theorem to H-spaces. Huang’s theorem also extends the corresponding result of Cuong in [5] to H-spaces. In [6], Ding and Tan extended the Fan-Browder fixed theorem to non-compact domain. In this note, we first give a new fixed point theorem which unifies and generalizes Huang’s theorem and Ding-Tan’s theorem mentioned above. The theorem is then further applied to prove an equilibrium existence theorem which improves and generalizes corresponding result obtained by Cubiotti and Nordo in [4]. In order to establish our results, we give some definitions and notations. Throughout this paper we use 2 and F (S) to denote the family of all subsets and the family of all nonempty finite subsets of a set S, respectively; and suppose all topological spaces are Hausdorff. Let A be a subset of a topological space X.We use A to denote the closure of A in X.Let X be a topological space and F (X) the family of all nonempty finite subsets of X.Let {Γ } be a family of some nonempty contractible subsets of X...
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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-003-0117-z
Publisher site
See Article on Publisher Site

Abstract

In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 3, 2017

References

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