Let (X,H) be a pair of a smooth rational surface X and an ample divisor H on X . Assume that (KX , H) < 0. Let MH(r, c1, χ) be the moduli space of semi-stable sheaves E of rk(E) = r, c1(E) = c1 and χ(E) = χ. To consider relations between moduli spaces of different invariants is an interesting problem. If (c1, H) = 0 and χ ≤ 0, then Maruyama [Ma2], [Ma3] studied such relations and constructed a ...

The submartingale convergence theorem is often described as a stochastic analogue to the bounded convergence theorem for monotone sequences of real numbers. We define an alternative process which is a stochastic analogue to an iterative contraction process. A general convergence theorem is presented, with an extension to multivariate processes. The convergence theorem functions in a manner simi...

We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, we introduce a cone generalized semi-cyclicφ−contraction maps and prove best proximity points theorems for such mapsin cone metric spaces. Also, we study existence and convergence results ofbest proximity points of such maps in normal cone metric spaces. Our resultsgeneralize some results on the topic.

In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.