In this paper, a new class of fuzzy topological spaces called ordered fuzzy pre-extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy pre-extremally disconnected spaces has been discussed as in [9] besides proving several other propositions and lemmas.

The purpose of this paper is to prove common fixed point theorem for multivalued mappings satisfying some conditions in intuitionistic fuzzy metric space in the sense of Alaca et al.

We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss $M{\ddot{o}}nch$ Kakutani and contractive type maps.

Let {${\xi}_j;j\;{\geq}\;1$} be a centered strictly stationary random sequence defined by $S_0\;=\;0$, $S_n\;=\;\Sigma^n_{j=1}\;{\xi}_j$ and $\sigma(n)\;=\;33\sqrt {ES^2_n}$ where $\sigma(t),\;t\;>\;0$, is a nondecreasing continuous regularly varying function. Suppose that there exists $n_0\;{\geq}\;1$ such that, for any $n\;{\geq}\;n_0$ and $0\;{\leq}\;{\varepsilon}\;<\;1$, there exist positive constants $c_1$ and $c_2$ such that $c_1e^{-(1+{\varepsilon})x^2/2}\;{\leq}\;P\{\frac{{\mid}S_n{\mid}}{\sigma(n)}\;{\geq}\;x\}\;{\leq}\;c_2e^{-(1-{\varepsilon})x^2/2$, $x\;{\geq}\;1$ Under some additional conditions, we investigate some limsup results for the increments of partial sum processes of the sequence {${\xi}_j;j\;{\geq}\;1$}.

Let $r\;{\geq}\;q$. We get the stability of the estimates of the $\bar{\partial}$-Neumann problem for (p, r)-forms on a weakly q-convex complex submanifold. As a by-product of the stability of the $\bar{\partial}$-estimates, we get the Mergelyan approximation property for (p, r)-forms on a weakly q-convex complex submanifold which satisfies property (P).

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

We recently showed in [5] a semilocal convergence theorem that guarantees convergence of Newton's method to a locally unique solution of a nonlinear equation under hypotheses weaker than those of the Newton-Kantorovich theorem [7]. Here, we first weaken Miranda's theorem [1], [9], [10], which is a generalization of the intermediate value theorem. Then, we show that operators satisfying the weakened Newton-Kantorovich conditions satisfy those of the weakened Miranda’s theorem.

We approximate a locally unique solution of a nonlinear operator equation containing a non-differentiable operator in a Banach space setting using Newton's method. Sufficient conditions for the semilocal convergence of Newton's method in this case have been given by several authors using mainly increasing sequences [1]-[6]. Here, we use center as well as Lipschitz conditions and decreasing majorizing sequences to obtain new sufficient convergence conditions weaker than before in many interesting cases. Numerical examples where our results apply to solve equations but earlier ones cannot [2], [5], [6] are also provided in this study.

The purpose of this paper is to study the existence and uniqueness of the fixed point of uniformly pseudo-contractive operator and the solution of equation with uniformly accretive operator, and to approximate the fixed point and the solution by the Mann iterative sequence in an arbitrary Banach space or an uniformly smooth Banach space respectively. The results presented in this paper show that if X is a real Banach space and A : X $\rightarrow$ X is an uniformly accretive operator and (I-A)X is bounded then A is a mapping onto X when A is continuous or $X^*$ is uniformly convex and A is demicontinuous. Consequently, the corresponding results which depend on the assumptions that the fixed point of operator and solution of the equation are in existence are improved.