Optimal combinations bounds of root-square and arithmetic means for Toader mean

Sharp approximations for the complete elliptic integrals of the second kind by one-parameter means

“…is valid for r ∈ (0, 1). Other various approximations for E (r) can be found in [10], [24], [18], [9], [25], [26], [27], [29], [28], [30], [31], [32], [33], [34] and references therein.…”

A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean

“…for all r ∈ (0, 1). In [9] it was pointed out that the bounds in (4.1) for E(r) are better than the bounds in (4.2) for some r ∈ (0, 1).…”

“…Recently, Toader mean has attracted attention of several researchers. In particular, many remarkable inequalities for T (a, b) can be found in the literature [6,7,9,10,17]. It was conjectured in [16] that…”

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

“…Recently, the mean value theory has been the subject of intensive research, and many remarkable inequalities and properties for various bivariate means can be found in the literature [28][29][30][31][32][33].…”