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On lattice-valued maps stemming from the notion of optimal average

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Abstract

The main purpose of this paper is to study certain lattice-valued maps through associated functional equations and inequalities. We deal with morphisms between an algebraic structure and an ordered structure. Next, we solve a separation problem for the inequalities studied. Moreover, we discuss the Hyers-Ulam stability of our main equation. Our research is motivated by the notion of optimal average, which was introduced by the first author in 1994.

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Authors and Affiliations

  1. Institute of Mathematics, University of Miskolc, 3515, Miskolc-Egyetemváros, Hungary

    N. K. Agbeko

  2. Institute of Mathematics, Łódź University of Technology, ul. Wólczańska 215, 93-005, Łódź, Poland

    W. Fechner

  3. Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, Poland

    E. Rak

Authors
  1. N. K. Agbeko
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  2. W. Fechner
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  3. E. Rak
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Corresponding author

Correspondence to W. Fechner.

Additional information

The first author was supported by the Center of Excellence of Mechatronics and Logistics at he University of Miskolc.

The third author was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge No. RPPK. 01.03.00-18-001/10.

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Agbeko, N.K., Fechner, W. & Rak, E. On lattice-valued maps stemming from the notion of optimal average. Acta Math. Hungar. 152, 72–83 (2017). https://doi.org/10.1007/s10474-017-0719-1

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  • DOI: https://doi.org/10.1007/s10474-017-0719-1

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