For a holomorphic one-form $${\xi }$$ on weakly 1-complete manifold X with certain properties, we will discuss the connectivity of pair $$(\hat{X},F^{-1}(z))$$ , where $$\pi :\hat{X} \rightarrow X$$ is covering map and F function $$\hat{X}$$ such that $$dF=\pi ^*{\xi . We also criteria about when admits proper mapping onto Riemann surface.

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

and Applied Analysis 3 Proposition 1.7 see 6 . Let X,G be a G-metric space. Then the followings are equivalent. 1 The sequence {xn} is G-Cauchy; 2 For every > 0, there exists k ∈ N such that G xn, xm, xm < , for all n,m ≥ k. Proposition 1.8 see 6 . Let X,G be a G-metric space. Then the function G x, y, z is jointly continuous in all three of its variables. Definition 1.9 see 6 . Let X,G and X′,...

Let f0,∞={fn}n=0∞ be a sequence of continuous self-maps on compact metric space X. The nonautonomous dynamical system (X,f0,∞) induces the set-valued (K(X),f¯0,∞) and fuzzified (F(X),f˜0,∞). We prove that under some natural conditions, positive topological entropy implies infinite (F(X),f˜0,∞), respectively; zero (S1,f0,∞) invariant subsystems (K(S1),f¯0,∞) (F(S1),f˜0,∞), respectively. confirm ...

The main usage of supermodular functions is to cross out tight sets, that is to use only the following important property. The intersection and the union of two sets with a maximal function value also have maximal function value. But for this purpose we do not need the full strength of supermodularity, some weaker concept suffices. We introduce here a new property, the so called λsupermodularit...

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...