In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of real-valued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence and study statistical analogue of convergence and Cauchy criterion for double sequences of real-valued ...

It is well-known that on quasi-pseudometric space $(X,q)$, every $q^s$-Cauchy sequence left (or right) $K$-Cauchy but the converse does not hold in general. In this article, we study a class of maps preserve (right) sequences call sequentially-regular maps. Moreover, characterize totally bounded sets terms and right uniformly locally semi-Lipschitz

To every Darboux integrable system there is an associated Lie group G which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the Vessiot group G. If the Vessiot group G is solvable then the Cauchy problem can...

In this article, we introduce the notion of statistically pre-Cauchy double sequence of fuzzy numbers. Then we present a characterization of the class of bounded statistically pre-Cauchy double sequences of fuzzy numbers with the help of Orlicz function. Further, we present a characterization of the class of bounded statistically convergent double sequences of fuzzy numbers and linked with Cesà...

and Applied Analysis 3 Lemma 3. Let {x k } and {z k } be any sequence generated by Algorithm 1. Suppose that g is monotone and that the solution set of (1) is not empty, then {x k } and {z k } are both bounded. Furthermore, it holds that lim k→∞ 󵄩󵄩󵄩󵄩xk − zk 󵄩󵄩󵄩󵄩 = 0, (13) lim k→∞ 󵄩󵄩󵄩󵄩xk+1 − xk 󵄩󵄩󵄩󵄩 = 0. (14) Proof. From (6), we have ⟨g (z k ) , x k − z k ⟩ = −α k ⟨g (z k ) , d k ⟩ ≥ σα 2 k 󵄩󵄩󵄩󵄩...

We say a functional equation () is stable if any function g satisfying the equation () approximatelyis near to true solution of (). Using xed point methods, we investigate approximately higherternary derivations in Banach ternary algebras via the Cauchy functional equationf(1x + 2y + 3z) = 1f(x) + 2f(y) + 3f(z) :

In this paper, we introduce the concept of λ-statistically Cauchy sequence of fuzzy numbers and show that it is equivalent to λ-statistically convergent sequence of fuzzy numbers. AMS Subject Classification: 40A05, 40C05, 40D05

Abstract In this paper, we present the ideal convergence of triple sequences for rough variables. Furthermore, sequence plays an extremely important role in fundamental theory mathematics. This paper presents two types sequence: Convergence trust and mean. Some mathematical properties those new concepts are also given. addition, introduce Cauchy spaces.