scholarly journals Further Improved Weighted Arithmetic-Geometric Operator Mean Inequalities

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 823
Author(s):  
Jianming Xue ◽  
Xingkai Hu
Keyword(s):  
Weighted Arithmetic ◽  
Operator Mean ◽  
Geometric Operator

The main purpose of this paper is to present some weighted arithmetic-geometric operator mean inequalities. These inequalities are refinements and generalizations of the corresponding results. An example is provided to confirm the effectiveness of the results.

The Schwarz inequality via operator-valued inner product and the geometric operator mean

2019 ◽  
Vol 561 ◽  
pp. 141-160 ◽  
Author(s):  
Masayuki Fujimoto ◽  
Yuki Seo
Keyword(s):  
Schwarz Inequality ◽  
Inner Product ◽  
Operator Mean ◽  
Geometric Operator

Further inequalities involving the weighted geometric operator mean and the Heinz operator mean

2021 ◽  
pp. 1-23
Author(s):  
Ibrahim Ahmed Al-Subaihi ◽  
Mustapha Raïssouli
Keyword(s):  
Operator Mean ◽  
Geometric Operator

On a functional mean inequality, application for the geometric operator mean

2015 ◽  
Vol 9 ◽  
pp. 1165-1171
Author(s):  
Rabie Zine ◽  
Mustapha Raissouli
Keyword(s):  
Operator Mean ◽  
Geometric Operator

FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES

2017 ◽  
Vol 96 (3) ◽  
pp. 496-503 ◽  
Author(s):  
MUSTAPHA RAÏSSOULI
Keyword(s):  
Relative Entropy ◽  
Upper Bound ◽  
Functional Inequality ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Functional Inequalities ◽  
Weighted Arithmetic ◽  
Related Operator ◽  
Operator Mean

We present refined and reversed inequalities for the weighted arithmetic mean–harmonic mean functional inequality. Our approach immediately yields the related operator versions in a simple and fast way. We also give some operator and functional inequalities for three or more arguments. As an application, we obtain a refined upper bound for the relative entropy involving functional arguments.

scholarly journals Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

2021 ◽  
Author(s):  
Faruk Karaaslan ◽  
Mohammed Allaw Dawood Dawood
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Two Dimensional ◽  
Weighted Arithmetic ◽  
Mcdm Method ◽  
Dombi Operations

AbstractComplex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

scholarly journals Order of operators determined by operator mean

2015 ◽  
Vol 67 (1) ◽  
pp. 39-50
Author(s):  
Masaru Nagisa ◽  
Mitsuru Uchiyama
Keyword(s):  
Operator Mean

EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW

2017 ◽  
Vol 59 (3) ◽  
pp. 743-751
Author(s):  
SHOUWEN FANG ◽  
FEI YANG ◽  
PENG ZHU
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Ricci Flow ◽  
Compact Riemannian Manifold ◽  
Laplacian Operator ◽  
Witten Laplacian ◽  
Normalized Ricci Flow ◽  
Geometric Operator

AbstractLet (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Ricci flow. In the paper, we prove that the eigenvalues of geometric operator −Δφ + $\frac{R}{2}$ are non-decreasing under the Ricci flow for manifold M with some curvature conditions, where Δφ is the Witten Laplacian operator, φ ∈ C2(M), and R is the scalar curvature with respect to the metric g(t). We also derive the evolution of eigenvalues under the normalized Ricci flow. As a consequence, we show that compact steady Ricci breather with these curvature conditions must be trivial.

On strengthened weighted Carleman's inequality

2003 ◽  
Vol 68 (3) ◽  
pp. 481-490 ◽  
Author(s):  
Aleksandra Čižmešija ◽  
Josip Pecarić ◽  
Lars–Erik Persson
Keyword(s):  
Geometric Mean ◽  
Weighted Arithmetic ◽  
Carleman’S Inequality ◽  
Carleman's Inequality

In this paper we prove a new refinement of the weighted arithmetic-geometric mean inequality and apply this result in obtaining a sharpened version of the weighted Carleman's inequality.

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