| Summary: | In a personal communication, Prof. Domínguez Benavides noted that a fixed-point theorem for modular nonexpansive mappings in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mrow><mi>p</mi><mo>(</mo><mo>·</mo><mo>)</mo></mrow></msup><mrow><mo>(</mo><mi mathvariant="normal">Ω</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> obtained under the assumptions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mo>+</mo></msub><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula> and the property <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> satisfied by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> will force <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mo>−</mo></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>. Therefore, the conclusion is well known. In this note, we establish said conclusion without the assumption <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mo>+</mo></msub><mo><</mo><mo>∞</mo></mrow></semantics></math></inline-formula>.
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