The purpose of this paper is to investigate the following invariance equation involving two 2-variable generalized Bajraktarević means, i.e., we aim solve functional $$f^{-1}\Bigl(\frac{p_1(x)f(x) +p_2(y)f(y)}{p_1(x)+p_2(y)}\Bigr)+g^{-1}\Bigl(\frac{q_1(x)g(x) +q_2(y)g(y)}{q_1(x)+q_2(y)}\Bigr)=x + y \ (x,y\in I),$$ where I a nonempty open real interval and $$f,g \colon \to\mathbb{R}$$ are contin...

The recently developed magnetic resonance imaging (MRI) proton density fat fraction (PDFF) allows measurement of the fat in all segments of hepatic tissue. However, it is time consuming and inconvenient to measure each segment repeatedly. Moreover, volume of each segment also should be adjusted with arithmetic mean of the selected segments when total amount of liver fat is estimated. Therefore,...

Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have imp...

This paper measures the mean, standard deviation, alpha, and beta of venture capital investments, using a maximum likelihood estimate that corrects for selection bias. The biascorrected estimation neatly accounts for log returns. It reduces the estimate of the mean log return from 108% to 15%, and of the log market model intercept from 92% to 7%: The selection bias correction also dramatically ...

We prove the Murphy and Cohen’s conjecture that the maximum number of collisions of n + 1 elastic particles moving freely on a line is n(n+1) 2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate neighbors. In fact, we prove the stronger result that, for the same conclusion, the condition no interior particle has mass less than the geometric mean, rathe...

We find the greatest value λ and the least value μ such that the double inequality C(λa + (1 − λ)b, λb+ (1 − λ)a) < αA(a, b) + (1 − α)T (a, b) < C(μa + (1 − μ)b, μb+ (1− μ)a) holds for all α ∈ (0, 1) and a, b > 0 with a 6= b, where C(a, b), A(a, b), and T (a, b) denote respectively the contraharmonic, arithmetic, and Toader means of two positive numbers a and b.

For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively. In this paper, we present new sharp bounds for Seiffert P in terms of weighted power means of arithmetic mean A and geometric mean G : ( 2 3 A p1 + 3 G p1 )1/p1 < P < ( 2 3 A p2 + 3 G p2 )1/p2 , where p1 = 4/5 and p2 = logπ/2 (3/2)...