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May 18, 2026Aequationes Mathematicae0 citationsOpen Access

On continuous solutions of a generalized Gołab–Schinzel functional inequality

EJEliza JabłońskaUniversity of Agriculture in KrakowZŻZuzanna ŻurekJan Kochanowski University

Key Points

  • The aim is to enhance earlier results related to the Gołab–Schinzel inequality and to explore the properties of generalized solutions.
  • Improvement of results from prior research regarding the Gołab–Schinzel inequality.
  • Analysis of properties of solutions to generalized inequalities involving two continuous functions.
  • Investigation of conditions under which the function g is greater than or equal to function f.
  • The improved results demonstrate stronger bounds under the Gołab–Schinzel inequality.
  • New insights are provided on the relationship between functions f and g within the generalized inequality framework.

Abstract

In the paper we improve some results from 9 concerning the Goła̧b–Schinzel inequality f (x+f (x) y) f (x) f (y) for a continuous unknown function f: R R. We also show some properties of solutions of the generalized inequality f (x+g (x) y) f (x) f (y) for continuous unknown functions f, g: R R provided g f.

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Cite This Study

Jabłońska et al. (2026) studied this question.

synapsesocial.com/papers/6a0aaccf5ba8ef6d83b703ebhttps://doi.org/10.1007/s00010-026-01299-1
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