scholarly journals Stolarsky Means in Many Variables

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1320
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Stolarsky Means

We give in this article two possible explicit extensions of Stolarsky means to the multi-variable case. They attain all main properties of Stolarsky means and coincide with them in the case of two variables.

scholarly journals Global Bounds for the Generalized Jensen Functional with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2105
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Power Mean ◽  
Jensen Functional ◽  
Exact Bounds ◽  
Harmonic Means ◽  
Stolarsky Means ◽  
Generalized Arithmetic

In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means.

scholarly journals An Extension of Stolarsky Means to the Multivariable Case

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Slavko Simic
Keyword(s):  
Probability Theory ◽  
Stolarsky Means

We give an extension of well-known Stolarsky means to the multivariable case in a simple and applicable way. Some basic inequalities concerning this matter are also established with applications in Analysis and Probability Theory.

scholarly journals Stolarsky Means and Hadamard's Inequality

1998 ◽  
Vol 220 (1) ◽  
pp. 99-109 ◽  
Author(s):  
C.E.M. Pearce ◽  
J. Pečarić ◽  
V. Šimić
Keyword(s):  
Hadamard’S Inequality ◽  
Stolarsky Means

scholarly journals Jensen Functional, Quasi-Arithmetic Mean and Sharp Converses of Hölder’s Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3104
Author(s):  
Slavko Simić ◽  
Vesna Todorčević
Keyword(s):  
Generating Function ◽  
Hölder’S Inequality ◽  
Arithmetic Mean ◽  
Hölder's Inequality ◽  
Power Means ◽  
Jensen Functional ◽  
Exact Bounds ◽  
Stolarsky Means

In this article, we give sharp two-sided bounds for the generalized Jensen functional Jn(f,g,h;p,x). Assuming convexity/concavity of the generating function h, we give exact bounds for the generalized quasi-arithmetic mean An(h;p,x). In particular, exact bounds are determined for the generalized power means in terms from the class of Stolarsky means. As a consequence, some sharp converses of the famous Hölder’s inequality are obtained.

scholarly journals Non-symmetric Stolarsky means

2013 ◽  
pp. 227-237 ◽  
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Atiq Ur Rehman
Keyword(s):  
Stolarsky Means

scholarly journals Functional Stolarsky means

1999 ◽  
pp. 479-489
Author(s):  
Charles E. M. Pearce ◽  
Josip Pečarić ◽  
Vida Šimić
Keyword(s):  
Stolarsky Means

Schur power convexity of Stolarsky means

2012 ◽  
Vol 80 (1-2) ◽  
pp. 43-66
Author(s):  
Zhen-Hang Yang
Keyword(s):  
Stolarsky Means

scholarly journals Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator

2021 ◽  
Author(s):  
Martin Heida ◽  
Markus Kantner ◽  
Artur Stephan
Keyword(s):  
Finite Volume ◽  
Numerical Experiments ◽  
Point Of View ◽  
Weight Functions ◽  
Convergence Properties ◽  
Finite Volume Discretization ◽  
Discretization Schemes ◽  
Stolarsky Means ◽  
Fokker Planck

We introduce a family of various finite volume discretization schemes for the Fokker–Planck operator, which are characterized by different Stolarsky weight functions on the edges. This family particularly includes the well-established Scharfetter–Gummel discretization as well as the recently developed square-root approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the choice of the Stolarsky weights. We show that the Scharfetter–Gummel scheme has the analytically best convergence properties but also that there exists a whole branch of Stolarsky means with the same convergence quality. We show by numerical experiments that for small convection the choice of the optimal representative of the discretization family is highly non-trivial while for large gradients the Scharfetter–Gummel scheme stands out compared to the others.

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