Abstract. Let p ∈ R , M be a bivariate mean, and Mp be defined by Mp(a,b) = M1/p(ap,bp) (p = 0) and M0(a,b) = limp→0 Mp(a,b) . In this paper, we prove that the sharp inequalities L2(a,b) < P(a,b) < NS1/2(a,b) < He(a,b) < A2/3(a,b) < I(a,b) < Z1/3(a,b) < Y1/2(a,b) hold for all a,b > 0 with a = b , where L(a,b) = (a− b)/(loga − logb) , P(a,b) = (a− b)/[2arcsin((a−b)/(a+b))] , NS(a,b) = (a−b)/[2ar...

The role of the topological index, ZG, proposed by the present author in 1971, in various problems and topics in elementary mathematics is introduced, namely, (i) Pascal’s and asymmetrical Pascal’s triangle, (ii) Fibonacci, Lucas, and Pell numbers, (iii) Pell equation, (iv) Pythagorean, Heronian, and Eisenstein triangles. It is shown that all the algebras in these problems can be easily obtaine...

The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if values arguments functions sin x, cos tg x and ctg expressed in radians, are algebraic numbers, then these transcendental numbers. Hence, it follows all angles pseudo-Heronian triangle, including Pythagoras or Heron If equal = r 2 \pi, where rational should be noted this case argument 2...

In the power battery industry, selection of an appropriate sustainable recycling supplier (SCS) is a significant topic in circular supply chain management. Evaluating and selecting SCS for spent batteries considered complex multi-attribute group decision-making (MAGDM) problem closely related to environment, economy, society. The linguistic T-spherical fuzzy (Lt-SF) set (Lt-SFS) combination ter...

Decision-making problems involve imprecise and incomplete information that can be modelled well using intuitionistic fuzzy numbers (IFNs). Various IFNs are available in the literature for modelling such problems. However, trapezoidal (TrIFNs) widely used. It is mainly because of flexibility capturing incompleteness occurs data. Aggregation operators play a vital role real-life decision-making (...

During the COVID-19 pandemic, masks have become essential items for all people to protect themselves from virus. Because of considering multiple factors when selecting an antivirus mask, decision-making process has more complicated. This paper proposes integrated approach that uses F-BWM-RAFSI methods mask selection with respect pandemic. Finally, sensitivity analysis was demonstrated by evalua...