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## On Jensen's inequality involving averages of convex functions

Roqia, Ghulam; Jakšetić, Julije; Pečarić, Josip;
On Jensen's inequality involving averages of convex functions // Sarajevo Journal of Mathematics,, 8 (2012), 20; 53-68 (podatak o recenziji nije dostupan, članak, znanstveni)

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Naslov
On Jensen's inequality involving averages of convex functions

Autori
Roqia, Ghulam ; Jakšetić, Julije ; Pečarić, Josip ;

Izvornik
Sarajevo Journal of Mathematics, (1840-0655) 8 (2012), 20; 53-68

Ključne riječi
Jensen’s inequality; log-convex function; exponential convexity

Sažetak
Using Wulbert result from [18] we deduce a method for constructing exponentially convex functions. To this date there is no known operative criteria for recognizing exponentially convex functions, so our method is of a special interest since there is a lack of examples of this class of functions. Constructed exponentially convex functions are then used for the construction of two and three parameters Cauchy means, that have the very nice property: they have the monotonicity property in their defining parameters. Particularly, we generalize recent results on Cauchy means from [2] and [4].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekti:
117-1170889-0888 - Generalne nejednakosti i primjene (Pečarić, Josip, MZOS ) ( CroRIS)

Ustanove:
Tekstilno-tehnološki fakultet, Zagreb,

Profili:

Julije Jakšetić (autor)

Josip Pečarić (autor)

#### Citiraj ovu publikaciju:

Roqia, Ghulam; Jakšetić, Julije; Pečarić, Josip;
On Jensen's inequality involving averages of convex functions // Sarajevo Journal of Mathematics,, 8 (2012), 20; 53-68 (podatak o recenziji nije dostupan, članak, znanstveni)
Roqia, G., Jakšetić, J., Pečarić, J. & (2012) On Jensen's inequality involving averages of convex functions. Sarajevo Journal of Mathematics,, 8 (20), 53-68.
@article{article, author = {Roqia, Ghulam and Jak\v{s}eti\'{c}, Julije and Pe\v{c}ari\'{c}, Josip}, year = {2012}, pages = {53-68}, keywords = {Jensen’s inequality, log-convex function, exponential convexity}, journal = {Sarajevo Journal of Mathematics,}, volume = {8}, number = {20}, issn = {1840-0655}, title = {On Jensen's inequality involving averages of convex functions}, keyword = {Jensen’s inequality, log-convex function, exponential convexity} }
@article{article, author = {Roqia, Ghulam and Jak\v{s}eti\'{c}, Julije and Pe\v{c}ari\'{c}, Josip}, year = {2012}, pages = {53-68}, keywords = {Jensen’s inequality, log-convex function, exponential convexity}, journal = {Sarajevo Journal of Mathematics,}, volume = {8}, number = {20}, issn = {1840-0655}, title = {On Jensen's inequality involving averages of convex functions}, keyword = {Jensen’s inequality, log-convex function, exponential convexity} }

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