Extensions of interpolation between the arithmetic-geometric mean inequality for matrices by Mojtaba Bakherad, Rahmatollah Lashkaripour, Monire Hajmohamadi

Subjects: “…arithmetic-geometric mean…”
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Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means by Yu-Ming Chu, Miao-Kun Wang

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Optimal Bounds for Gaussian Arithmetic-Geometric Mean with Applications to Complete Elliptic Integral by Hua Wang, Wei-Mao Qian, Yu-Ming Chu

“…We present the best possible parameters α1,β1,α2,β2∈R and α3,β3∈(1/2,1) such that the double inequalities Qα1(a,b)A1-α1(a,b)<AG[A(a,b),Q(a,b)]<Qβ1(a,b)A1-β1(a,b), α2Q(a,b)+(1-α2)A(a,b)<AG[A(a,b),Q(a,b)]<β2Q(a,b)+(1-β2)A(a,b), Q[α3a+(1-α3)b,α3b+(1-α3)a]<AG[A(a,b),Q(a,b)]<Q[β3a+(1-β3)b,β3b+(1-β3)a] hold for all a,b>0 with a≠b, where A(a,b), Q(a,b), and AG(a,b) are the arithmetic, quadratic, and Gauss arithmetic-geometric means of a and b, respectively. As applications, we find several new bounds for the complete elliptic integrals of the first and second kind.…”
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Refining and reversing the weighted arithmetic–geometric mean inequality involving convex functionals and application for the functional entropy by Mustapha Raïssouli, Mashael Almozini

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Calculation of integrals in MathPartner by Gennadi I. Malaschonok, Alexandr V. Seliverstov

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A Rational Approximation for the Complete Elliptic Integral of the First Kind by Zhen-Hang Yang, Jing-Feng Tian, Ya-Ru Zhu

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A new analogue of Gauss' functional equation by Hiroshi Haruki, Themistocles M. Rassias

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Fifth-order AGM-formula for the period of a large-angle pendulum by Akuro Big-Alabo

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The generalized circular intuitionistic fuzzy set and its operations by Dian Pratama, Binyamin Yusoff, Lazim Abdullah, Adem Kilicman

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Fractional Hermite–Hadamard, Newton–Milne, and Convexity Involving Arithmetic–Geometric Mean-Type Inequalities in Hilbert and Mixed-Norm Morrey Spaces <i>ℓ</i>_q(·)(M_p(·),v(·)) with Variable Exponents by Waqar Afzal, Mujahid Abbas, Daniel Breaz, Luminiţa-Ioana Cotîrlă

“…Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. …”
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Extension of Hu Ke's inequality and its applications by Tian Jing-Feng

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Generalizing the arithmatic geometric mean — a hapless computer experiment by Jaak Peetre

“…The paper discusses the asymptotic behavior of generalizations of the Gauss's arithmetic-geometric mean, associated with the names Meissel (1875) and Borchardt (1876). …”
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A Gauss type functional equation by Silvia Toader, Themistocles M. Rassias, Gheorghe Toader

“…Gauss' functional equation (used in the study of the arithmetic-geometric mean) is generalized by replacing the arithmetic mean and the geometric mean by two arbitrary means.…”
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Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series by B. R. Srivatsa Kumar, Shruthi, D. Anu Radha

“…Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’ theta functions.…”
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A symmetric splitting method for rigid body dynamics by E. Celledoni, N. Säfström

“…It has been known since the time of Jacobi that the solution to the free rigid body (FRB) equations of motion is given in terms of a certain type of elliptic functions. Using the Arithmetic-Geometric mean algorithm, (1), these functions can be calculated efficiently and accurately. …”
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Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities by Balakrishnan Sudha, George E. Chatzarakis, Ethiraju Thandapani

“…The results are obtained first by applying the arithmetic–geometric mean inequality along with the linearization method and then using comparison method as well as the integral averaging technique. …”
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Jessen's functional, its properties and applications by Lovričević Neda, Pečarić Josip, Krnić Mario

“…In particular, we obtain the whole series of refinements and converses of numerous classical inequalities such as the arithmetic-geometric mean inequality, Young's inequality and Hölder's inequality…”
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Determining Compensation Circuit Values to Minimize Leakage Magnetic Field in Wireless Power Transfer Systems with Double-Sided LCC Topology by Yujun Shin, Seongho Woo

“…The proposed method for calculating compensation circuit values is obtained through mathematical derivation using arithmetic–geometric mean inequality and verified through simulation and experimentation. …”
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Interval Oscillation Criteria for Second-Order Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals by Yuangong Sun

“…By using a generalized arithmetic-geometric mean inequality on time scales, we study the forced oscillation of second-order dynamic equations with nonlinearities given by Riemann-Stieltjes integrals of the form [p(t)ϕα(xΔ(t))]Δ+q(t)ϕα(x(τ(t)))+∫aσ(b)r(t,s)ϕγ(s)(x(g(t,s)))Δξ(s)=e(t), where t∈[t0,∞)T=[t0,∞)  ⋂  T, T is a time scale which is unbounded from above; ϕ*(u)=|u|*sgn u; γ:[a,b]T1→ℝ is a strictly increasing right-dense continuous function; p,q,e:[t0,∞)T→ℝ, r:[t0,∞)T×[a,b]T1→ℝ, τ:[t0,∞)T→[t0,∞)T, and g:[t0,∞)T×[a,b]T1→[t0,∞)T are right-dense continuous functions; ξ:[a,b]T1→ℝ is strictly increasing. …”
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Achieving Fair Spectrum Allocation and Reduced Spectrum Handoff in Wireless Sensor Networks: Modeling via Biobjective Optimization by Sang-Seon Byun, Kimmo Kansanen, Ilangko Balasingham, Joon-Min Gil

“…To tackle this intractability, we first convexify the original problem using arithmetic-geometric mean approximation and logarithmic change of the decision variables and then deploy weighted Chebyshev norm-based scalarization method in order to collapse the multiobjective problem into a single objective one. …”
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