**Volume 10, Issue 1, pp 34--47**

**Publication Date**: 2017-01-26

**Sang-Eon Han**
- Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 54896, Republic of Korea.

The present paper studies almost fixed point property for digital spaces whose structures are induced by Marcus-Wyse (M-, for brevity) topology. In this paper we mainly deal with spaces X which are connected M-topological spaces withM-adjacency (MA-spaces or M-topological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects, denoted by Ob(MAC), are MA-spaces and morphisms are MA-maps between MA-spaces (for more details, see Section 3), and MTC a category of M-topological spaces as Ob(MTC) and M-continuous maps as morphisms of MTC (for more details, see Section 3). We prove that whereas any MA-space does not have the fixed point property (FPP for short) for any MA-maps, a bounded simple MA-path has the almost fixed point property (AFPP for short). Finally, we refer the topological invariant of the FPP for M-topological spaces from the viewpoint of MTC.

Digital topology, fixed point property, Marcus-Wyse topology, MA-map, MA-isomorphism, MA-homotopy, MA-space, MA-contractibility, M-topological graph, almost fixed point property.

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