Research Article Some Properties of Pythagorean Modulus
نویسندگان
چکیده
Recently, Gao introduced some moduli from Pythagorean theorem. In terms of these moduli, he got some sufficient conditions for a Banach space X to have uniform normal structure, which plays an import role in fixed-point theory. In this paper, we mainly discuss the moduli E (X) and f (X). Let X be a Banach space. By SX and BX we will denote the unit sphere and unit ball of X , respectively. For every nonnegative number , the Pythagorean moduli are given by [1, 2]
منابع مشابه
Random Sequences from Primitive Pythagorean Triples
This paper shows that the six classes of PPTs can be put into two groups. Autocorrelation and cross-correlation functions of the six classes derived from the gaps between each class type have been computed. It is shown that Classes A and D (in which the largest term is divisible by 5) are different from the other four classes in their randomness properties if they are ordered by the largest ter...
متن کاملNew Approaches to Pythagorean Fuzzy Averaging Aggregation Operators
In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.
متن کاملTrisection, Pythagorean Angles, and Gaussian Integers
Pythagorean angles, that is angles with rational sines and cosines, provide an interesting environment for studying the question of characterizing trisectable angles. The main result of this paper shows that a Pythagorean angle is trisectable if and only if it is three times some other Pythagorean angle. Using the Euclidean parametrization of Pythagorean angles, this result allows an effective ...
متن کاملPrime Pythagorean triangles
A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequence. We exhibit a chain of seven prime Pythagorean triangles and we include a brief discussion of ...
متن کاملSome Induced Averaging Aggregation Operators Based on Pythagorean Fuzzy Numbers
In this paper we present two new types aggregation operators such as, induced Pythagorean fuzzy ordered weighted averaging aggregation operator and induced Pythagorean fuzzy hybrid averaging aggregation operator. We also discuss of important properties of these proposed operators and construct some examples to develop these operators.
متن کامل