Fatih Nuray

Lacunary statistical convergence of double sequences of sets

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them.

On Asymptotically Lacunary Statistical Equivalent Set Sequences

This paper presents three definitions which are natural combination of the definitions of asymptotic equivalence, statistical convergence, lacunary statistical convergence, and Wijsman convergence. In addition, we also present asymptotically equivalent (Wijsman sense) analogs of theorems in Patterson and Savas (2006).

A characterization of holomorphic bivariate functions of bounded index

Abstract The following notion of bounded index for complex entire functions was presented by Lepson. function f(z) is of bounded index if there exists an integer N independent of z, such that max{l:0≤l≤N}|f(l)(z)|l!≥|f(n)(z)|n!for alln.

I-Convergence Of Sequences Of Fuzzy Numbers

\max\limits_{\{l: 0\leq l\leq N\}} \left \{ \frac{|{f^{(l)}(z)}|}{l!}\right \} \geq \frac{|{f^{(n)}(z)}|}{n!}\quad\text{for all}\,\, n.

Asymptotically Lacunary Statistical Equivalence of Double Sequences of Sets

The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers M and N such that M and N are the least integers such that max{(k,l):0,0≤k,l≤M,N}|f(k,l)(z,w)|k!l!≥|f(m,n)(z,w)|m!n!for allmandn.

Asymptotic I-Equivalence of Two Number Sequences and Asymptotic I-Regular Matrices

\max\limits_{\{(k,l): 0,0\leq k, l\leq M, N\}} \left \{ \frac{|{f^{(k,l)}(z,w)}|}{k!\,l!}\right \} \geq \frac{|{f^{(m,n)}(z,w)}|}{m!\,n!}\quad\text{for all}\,\, m \, \text{and}\,\, n.