The Converse of the Minkowski's Inequality Theorem and its Generalization

1990 ◽  
Vol 109 (3) ◽  
pp. 663 ◽  
Author(s):  
Janusz Matkowski
Keyword(s):  
Minkowski’S Inequality ◽  
Inequality Theorem

Convexity and Minkowski's Inequality

2005 ◽  
Vol 112 (8) ◽  
pp. 740-742
Author(s):  
Geoffrey Brown
Keyword(s):  
Minkowski’S Inequality

scholarly journals A converse of Minkowski's inequality

2000 ◽  
Vol 216 (1-3) ◽  
pp. 253-256
Author(s):  
Horst Alzer ◽  
Stephan Ruscheweyh
Keyword(s):  
Minkowski’S Inequality

The generalized Laguerre inequalities and functions in the Laguerre-Pólya class

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
George Csordas ◽  
Anna Vishnyakova
Keyword(s):  
Entire Function ◽  
Open Problem ◽  
A Priori ◽  
Sufficient Conditions ◽  
Class Definition ◽  
Lindelöf Theorem ◽  
Order And Type ◽  
Geometric Result ◽  
Real Entire Function ◽  
Inequality Theorem

AbstractThe principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and on a deep theorem of Lindelöf (Theorem 2.2). In case of the complex Laguerre inequalities (Theorem 3.2), the proof is sketched for it requires a slightly more delicate analysis. Section 3 concludes with some other cognate results, an open problem and a conjecture which is based on Cardon’s recent, ingenious extension of the Laguerre-type inequalities.

Convexity and Minkowski's Inequality

2005 ◽  
Vol 112 (8) ◽  
pp. 740
Author(s):  
Geoffrey Brown
Keyword(s):  
Minkowski’S Inequality

A (⋆, ∗)-Based Minkowski’s Inequality for Sugeno Fractional Integral of Order α > 0

2015 ◽  
Vol 18 (4) ◽  
Author(s):  
Azizollah Babakhani ◽  
Hamzeh Agahi ◽  
Radko Mesiar
Keyword(s):  
Fractional Integral ◽  
Fuzzy Measure ◽  
Minkowski’S Inequality ◽  
Fuzzy Integral ◽  
Binary Operations

AbstractWe first introduce the concept of Sugeno fractional integral based on the concept of g-seminorm. Then Minkowski’s inequality for Sugeno fractional integral of the order α > 0 based on two binary operations ⋆, ∗ is given. Our results significantly generalize the previous results in this field of fuzzy measure and fuzzy integral. Some examples are given to illustrate the results.

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