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- W4221086176 abstract "The purpose of this paper is to investigate the local and global comparison of two n -variable nonsymmetric generalized Bajraktarević means, i.e., to establish necessary as well as sufficient conditions in terms of the unknown functions f , g , p 1 , … , p n , q 1 , … , q n : I → R for the comparison inequality f − 1 ( p 1 ( x 1 ) f ( x 1 ) + ⋯ + p n ( x n ) f ( x n ) p 1 ( x 1 ) + ⋯ + p n ( x n ) ) ≤ g − 1 ( q 1 ( x 1 ) g ( x 1 ) + ⋯ + q n ( x n ) g ( x n ) q 1 ( x 1 ) + ⋯ + q n ( x n ) ) in local and global sense. Here I is a nonempty open real interval, x 1 , … , x n ∈ I , and f , g are assumed to be continuous, strictly monotone and p 1 , … , p n , q 1 , … , q n : I → R + are positive valued. Concerning the global comparison problem, the main result of the paper states that if f , g are differentiable functions with nonvanishing first derivatives and, for all i ∈ { 1 , … , n } , p i p 0 = q i q 0 and p 0 ( x ) ( f ( x ) − f ( y ) ) p 0 ( y ) f ′ ( y ) ≤ q 0 ( x ) ( g ( x ) − g ( y ) ) q 0 ( y ) g ′ ( y ) ( x , y ∈ I ) are satisfied (where p 0 : = p 1 + … + p n and q 0 : = q 1 + … + q n ), then the above comparison inequality holds for all x 1 , … , x n ∈ I ." @default.
- W4221086176 created "2022-04-03" @default.
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- W4221086176 date "2022-08-01" @default.
- W4221086176 modified "2023-09-24" @default.
- W4221086176 title "Local and global comparison of nonsymmetric generalized Bajraktarević means" @default.
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- W4221086176 doi "https://doi.org/10.1016/j.jmaa.2022.126172" @default.
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