Applications of the Fixed Point Index in Menger PN-Spaces

Chuanxi Zhu, Qiuying Li

Nanchang University, Republic of China

Abstract: In this paper, applications of the fixed-point index of a nonlinear operator in Menger PN-spaces are given. Theorems on the existence of fixed points of a compact continuous operator are obtained. At the same time, the existence of the solution of a class of differential equations in a complete Menger PN-space is studied, and the theorem on the existence of the solution of a class of differential equations is obtained.

Keywords: fixed-point index, probabilistic normed space, Menger PN-space, $T$-retraction, completeness, distribution function.

UDC: 517.988.523

Received: 03.03.2009

DOI: 10.4213/mzm8662

 English version: Mathematical Notes, 2012, 91:5, 725–730

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