Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean

Abstract

√3ν/(6ν) are the best possible parameters on the interval [1/2, 1] such that the double inequalitieshold for all x, y > 0 with x = y and ν ∈ [1/2, ∞), where A(x, y) is the arithmetic mean, C(x, y) is the contraharmonic mean, and R QA (x, y) and R AQ (x, y) are two Neuman means.

Some New Hermite–Hadamard-Type Inequalities Associated with Conformable Fractional Integrals and Their Applications

“…{ } for all a, b ∈ (0, ∞). Recently, the properties and applications for the bivariate means and their related special functions have attracted the attention of many researchers [83][84][85][86][87][88][89][90][91][92][93].…”

Inequalities Involving Conformable Approach for Exponentially Convex Functions and Their Applications

“…A bivariate function Ω: (0, ∞) × (0, ∞) ⟶ (0, ∞) is said to be a mean if min a, b { } ≤ Ω(a, b) ≤ max a, b { } for all a, b ∈ (0, ∞). Recently, the bivariate means have been the subject of intensive research [63][64][65][66][67][68][69][70][71][72][73][74][75]; in particular, many remarkable inequalities and properties for the bivariate means and their related special functions can be found in the literature [76][77][78][79][80][81][82][83][84][85].…”

Delay dynamic double integral inequalities on time scales with applications

“…Due to its vast contributions in different branches of mathematics, it attracts the researchers and mathematicians to work on it. The role of inequalities cannot be forgot because they have huge contributions in the theory of differential equations , bivariate means [23][24][25][26][27][28][29][30][31], calculation and optimization [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49], special functions [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69], probability and statistics [70][71]…”