Abstract
Walter and Weckesser’s result (Aequationes Math 46:212–219, 1993), extending the Bushell–Okrasiński convolution type inequality (Bushell and Okrasiński in J Lond Math Soc (2) 41:503–510, 1990), gave some general conditions on the functions \(k:\left[ 0,d\right) \rightarrow \mathbb {R}\) and \(g:\left[ 0,\infty \right) \rightarrow \mathbb {R}\) under which, for every increasing function f : \(\left[ 0,d\right) \rightarrow \left[ 0,\infty \right) \), the inequality
is satisfied. Applying the result on a simultaneous system of functional inequalities, we prove that if \(d>1,\) then, in general, both k and g must be power functions.
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Acknowledgements
The authors are indebted to Dr. Dorota Krassowska for her important remark. The authors would also like to thank the reviewer for his/her valuable comments and helpful suggestions.
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Dedicated to Professor Karol Baron on his 70th birthday.
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Małolepszy, T., Matkowski, J. On the special form of integral convolution type inequality due to Walter and Weckesser. Aequat. Math. 93, 9–19 (2019). https://doi.org/10.1007/s00010-018-0576-1
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DOI: https://doi.org/10.1007/s00010-018-0576-1