Taiwanese Journal of Mathematics

SOME FIXED-POINT THEOREMS ON AN ALMOST G-CONVEX SUBSET OF A LOCALLY G-CONVEX SPACE AND ITS APPLICATIONS

Chi-Ming Chen

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Abstract

In this paper, we first obtain the generalizations of the almost fixed point theorems on the almost $G$-convex sets and the Himmelberg fixed point theorems on a locally G-convex space. Next, we invoke non-convexity of constraint regions in place of convexity and we obtain the new fixed point theorems, "Let $X$ be an almost $G$-convex subset of a locally $G$-convex space $E$. If $T \in \Gamma^* - KKM(X,X)$ is compact and closed, then $T$ has a fixed point."

Article information

Source
Taiwanese J. Math., Volume 10, Number 3 (2006), 797-805.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403861

Digital Object Identifier
doi:10.11650/twjm/1500403861

Mathematical Reviews number (MathSciNet)
MR2206328

Zentralblatt MATH identifier
1110.47041

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54C60: Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20] 55M20: Fixed points and coincidences [See also 54H25]

Keywords
fixed point theorem almost $G$-convex sets locally $G$-convex space $\Gamma-KKM$ mapping $\Gamma^*-KKM$ property matching theorem quasi-equilibrium

Citation

Chen, Chi-Ming. SOME FIXED-POINT THEOREMS ON AN ALMOST G-CONVEX SUBSET OF A LOCALLY G-CONVEX SPACE AND ITS APPLICATIONS. Taiwanese J. Math. 10 (2006), no. 3, 797--805. doi:10.11650/twjm/1500403861. https://projecteuclid.org/euclid.twjm/1500403861


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References

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