In this article we define and investigate statistical analogue of convergence and Cauchy for double sequences in 2-normed space.We also obtain a criteria for a double sequence in 2-normed spaces to be a statistical Cauchy sequence. Mathematics Subject Classification: 40A05; 40A99, 46A70, 46A45

In this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. Meantime, an example is provided toillustrate this theorem. The main result shows that a self-mappingon a G-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. Afterwards, some results inco...

The present study introduces the concepts of ideal convergence (I-convergence), Cauchy (I-Cauchy) sequences, I *-convergence, and *-Cauchy sequences in intuitionistic fuzzy metric spaces. It defines I-limit I-cluster points as a sequence these Afterward, it examines some their basic properties. Lastly, paper discusses whether phenomena should be further investigated.

Intuitionistic set theory without choice axioms does not prove that every Cauchy sequence of rationals has a modulus of convergence, or that the set of Cauchy sequences of rationals is Cauchy complete. Several other related non-provability results are also shown.

In this paper we introduce and investigate I2-convergence, I∗ 2 -convergence, I2-limit points, and I2-cluster points of a double sequence in a fuzzy 2-normed linear space. We prove a decomposition theorem for I2-convergence of double sequences. The notions of I2-double Cauchy and I∗ 2 -double Cauchy sequence are defined, and some of their properties are studied.

The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed every real number r is replaced by a fuzzy number r either triangular fuzzy number or singleton fuzzy set fuzzy point . And then, we will consider that some results re...

In this paper, we introduce the concepts of I2-Cauchy, I∗ 2 -Cauchy double sequence of fuzzy numbers and study their some properties and relations, where I2 denotes the ideal of subsets of N× N.

We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.

Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g, we have the Cauchy-Schwarz inequality: 0.1 THEOREM (Cauchy-Schwarz inequality). Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g such that

and Applied Analysis 3 Definition 2.2 Kramosil and Michálek 3 . The triple X,M, ∗ is called a fuzzy metric space if X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set onX×X× 0,∞ satisfying the following conditions: for all x, y, z ∈ X and s, t > 0, FM-1 M x, y, 0 0, FM-2 M x, y, t 1 if and only if x y, FM-3 M x, y, t M y, x, t , FM-4 M x, y, t ∗M y, z, s ≤ M x, z, t s , FM-5 a...