Characterization of Monotone Sequences of Positive Numbers Prescribed by Means

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F25%3AA2603AZ7" target="_blank" >RIV/61988987:17310/25:A2603AZ7 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-7390/13/5/696" target="_blank" >https://www.mdpi.com/2227-7390/13/5/696</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math13050696" target="_blank" >10.3390/math13050696</a>

Result language

angličtina

Original language name

Characterization of Monotone Sequences of Positive Numbers Prescribed by Means

Original language description

The aim of this article is to investigate the relations between the exponent of the convergence of sequences and other characteristics defined for monotone sequences of positive numbers. Another main goal is to characterize such monotone sequences (an) of positive numbers that, for each n≥2, satisfy the equality an=K(an−1,an+1), where the function K:R+×R+→R+ is the mean, i.e., each value of K(x,y) lies between min{x,y} and max{x,y}. Well-known examples of such sequences are, for example, arithmetic (geometric) progression, because starting from the second term, each of its terms is equal to the arithmetic (geometric) mean of its neighboring terms. Furthermore, this accomplishment generalized and extended previous results, where the properties of the logarithmic sequence (an) are referred to, i.e., in such a sequence that every n≥2 satisfies an=L(an−1,an+1), where L(x,y) is the logarithmic mean of positive numbers x,y defined as follows: L(x,y):=y−xlny−lnxifx≠y,xifx=y.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10100 - Mathematics

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

2227-7390

Volume of the periodical

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Issue of the periodical within the volume

5

Country of publishing house

CH - SWITZERLAND

Number of pages

17

Pages from-to

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UT code for WoS article

001442511900001

EID of the result in the Scopus database

2-s2.0-86000509571