A mean value inequality for the cyclic functions

2021 ◽  
pp. 1-5
Author(s):  
Horst Alzer
Keyword(s):  
Mean Value ◽  
Mean Value Inequality

scholarly journals Generalized Geodesic Convexity on Riemannian Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 547 ◽  
Author(s):  
Izhar Ahmad ◽  
Meraj Ali Khan ◽  
Amira A. Ishan
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Global Minimum ◽  
Mean Value ◽  
Mathematical Programming Problem ◽  
Hadamard Manifolds ◽  
Geodesic Convexity ◽  
Invex Functions ◽  
Mean Value Inequality ◽  
Global Minimum Point

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

scholarly journals On a mean value inequality

1975 ◽  
Vol 81 (5) ◽  
pp. 950-954 ◽  
Author(s):  
Alberto Torchinsky
Keyword(s):  
Mean Value ◽  
Mean Value Inequality

scholarly journals MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS

2013 ◽  
Vol 55 (2) ◽  
pp. 349-368 ◽  
Author(s):  
OLEKSIY DOVGOSHEY ◽  
JUHANI RIIHENTAUS
Keyword(s):  
Sufficient Conditions ◽  
Continuous Functions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Subharmonic Functions ◽  
Mean Value Inequality ◽  
The Mean ◽  
Mean Value Inequalities ◽  
Necessary And Sufficient ◽  
Bounded Sets

AbstractThe mean value inequality is characteristic for upper semi-continuous functions to be subharmonic. Quasinearly subharmonic functions generalise subharmonic functions. We find the necessary and sufficient conditions under which subsets of balls are big enough for the characterisation of non-negative, quasinearly subharmonic functions by mean value inequalities. Similar result is obtained also for generalised mean value inequalities where, instead of balls, we consider arbitrary bounded sets, which have non-void interiors and instead of the volume of ball some functions depending on the radius of this ball.

scholarly journals A mean value inequality with applications to Bergman space operators

1996 ◽  
Vol 173 (2) ◽  
pp. 295-305 ◽  
Author(s):  
Patrick Ahern ◽  
Zeljko Cuckovic
Keyword(s):  
Bergman Space ◽  
Mean Value ◽  
Mean Value Inequality
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