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Pregled bibliografske jedinice broj: 593169

Uniform treatment of Jensen type inequalities


Pečarić, Josip; Perić, Ivan; Rodić Lipanović, Mirna
Uniform treatment of Jensen type inequalities // Mathematical reports, 16(66) (2014), 2; 183-205 (međunarodna recenzija, članak, znanstveni)


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Naslov
Uniform treatment of Jensen type inequalities

Autori
Pečarić, Josip ; Perić, Ivan ; Rodić Lipanović, Mirna

Izvornik
Mathematical reports (2285-3898) 16(66) (2014), 2; 183-205

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Green function; Jensen inequality; Hermite-Hadamard inequality

Sažetak
The main purpose of this paper is to give the uniform treatment of the Jensen type inequalities. Using the Green function, we give some new conditions for Jensen's inequality to hold. Integral and discrete case are presented. In the discrete version we get the generalization of the results from [A. McD. Mercer: An "error term" for the Ky Fan inequality, J. Math. Anal. Appl. 220 (1998), 774-777.] and [A. McD. Mercer: Some new inequalities involving elementary mean values, J. Math. Anal. Appl. 229 (1999), 677-681.], and in integral version the generalization of the results from [J. E. Pečarić, I. Perić, H. M. Srivastava: A family of the Cauchy type mean-value theorems, J. Math. Anal. Appl. 306 (2005) 730-739.]. Using the same method we also give adequate results for the converses of the Jensen inequality. As a consequence, also the results concerning the Hermite-Hadamard inequalities are presented.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Ustanove:
Prehrambeno-biotehnološki fakultet, Zagreb,
Tekstilno-tehnološki fakultet, Zagreb

Profili:

Avatar Url Mirna Rodić (autor)

Avatar Url Josip Pečarić (autor)

Avatar Url Ivan Perić (autor)

Citiraj ovu publikaciju:

Pečarić, Josip; Perić, Ivan; Rodić Lipanović, Mirna
Uniform treatment of Jensen type inequalities // Mathematical reports, 16(66) (2014), 2; 183-205 (međunarodna recenzija, članak, znanstveni)
Pečarić, J., Perić, I. & Rodić Lipanović, M. (2014) Uniform treatment of Jensen type inequalities. Mathematical reports, 16(66) (2), 183-205.
@article{article, year = {2014}, pages = {183-205}, keywords = {Green function, Jensen inequality, Hermite-Hadamard inequality}, journal = {Mathematical reports}, volume = {16(66)}, number = {2}, issn = {2285-3898}, title = {Uniform treatment of Jensen type inequalities}, keyword = {Green function, Jensen inequality, Hermite-Hadamard inequality} }
@article{article, year = {2014}, pages = {183-205}, keywords = {Green function, Jensen inequality, Hermite-Hadamard inequality}, journal = {Mathematical reports}, volume = {16(66)}, number = {2}, issn = {2285-3898}, title = {Uniform treatment of Jensen type inequalities}, keyword = {Green function, Jensen inequality, Hermite-Hadamard inequality} }

Časopis indeksira:


  • Web of Science Core Collection (WoSCC)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka::


  • MathSciNet
  • Zentrallblatt für Mathematik/Mathematical Abstracts





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