Positivity of sums and integrals for nnn-convex functions via the Fink identity

Asif R KHAN; Josip PECARIC; Marjan PRALJAK; Sanja VAROSANEC

Makale detayları

Positivity of sums and integrals for nnn-convex functions via the Fink identity

Yazarlar:

Asif R KHAN | Josip PECARIC | Marjan PRALJAK | Sanja VAROSANEC

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.579-594

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745635

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We consider the positivity of the sum ∑ni=1ρiϝ(ξi)∑i=1nρiϝ(ξi)\sum_{i=1}^n\rho_i\digamma(\xi_i), where ϝϝ\digamma is a convex function of higher order, as well as analogous results involving the integral ∫b0a0ρ(ξ)ϝ(g(ξ))dξ∫a0b0ρ(ξ)ϝ(g(ξ))dξ\int_{a_0}^{b_0}\rho(\xi)\digamma(g(\xi))d\xi. We use a representation of the function ϝϝ\digamma via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results.

Makale detayları

Positivity of sums and integrals for nnn-convex functions via the Fink identity

Yazarlar: Asif R KHAN | Josip PECARIC | Marjan PRALJAK | Sanja VAROSANEC

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.579-594

Belge Tipi: Makale

Yayın Tarihi: 3/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745635

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Asif R KHAN | Josip PECARIC | Marjan PRALJAK | Sanja VAROSANEC

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 2, pp.579-594

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745635

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098