In this paper, we introduce the concept of SPG*-closed mapping and continuous among which SPG-closed mappings, mappings SPG**-closed relationship between them, also SPG-continuous SPG*-continuous SPG**-continuous them. Among result obtain are concepts closed independent PG**-continuous independent.

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

In this paper, we compare the computability and complexity of a continuous real function F with the computability and complexity of the graph G of the function F . A similar analysis will be carried out for functions on subspaces of the real line such as the Cantor space, the Baire space and the unit interval. In particular, we de1ne four basic types of e"ectively closed sets C depending on whe...