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...

A 3-connected quadrangulation of a closed surface is said to be K′ 3-irreducible if no faceor cube-contraction preserves simplicity and 3-connectedness. In this paper, we prove that a K′ 3-irreducible quadrangulation of a closed surface except the sphere and the projective plane is either (i) irreducible or (ii) obtained from an irreducible quadrangulation H by applying 4-cycle additions to F0 ...

Let IIR be the set of closed and bounded intervals of real numbers. Arithmetic in IIR can be defined via the power set IPIR (the set of all subsets) of real numbers. If in case of division zero is not contained in the divisor arithmetic in IIR is an algebraically closed subset of the arithmetic in IPIR. Arithmetic in IPIR allows division by an interval that contains zero also. This results in c...

Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms f : CP → CP, when k > 1. Classical theory describes U(f) as the complement in CP of the support of a dynamically-defined closed positive (1, 1) current. Given any closed positive (1, 1) current S on CP, we give a definition of linking number between closed loops in CP \ suppS and the current S. It has ...

Little is known about the global topology of the Fatou set U(f) for holomorphic endomorphisms f : CP → CP, when k > 1. Classical theory describes U(f) as the complement in CP of the support of a dynamically-defined closed positive (1, 1) current. Given any closed positive (1, 1) current S on CP, we give a definition of linking number between closed loops in CP \ suppS and the current S. It has ...

Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...