Sixteen General Theorems of Cyclic Integral Inequalities
Abstract
This paper extends classical discrete cyclic inequalities to a continuous setting involving cyclic sequences of measurable functions. By integrating cyclic symmetry with functional analysis, we establish an integral inequality framework that provides global bounds on combinations of adjacent functional terms. Utilizing fundamental results including the Minkowski, Young, Cauchy-Schwarz, Hardy, and Jensen inequalities, we present sixteen general families of cyclic integral inequalities. Detailed proofs, special cases, and concluding remarks are also provided.
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References
Bencze, M., & Pop, O. T. (2011). Generalizations and refinements for Nesbitt's inequality. Journal of Mathematical Inequalities, 5(1), 13–20. https://doi.org/10.7153/jmi-05-02
Bencze, M., & Zhao, C. (2008). A refinement of Nesbitt's inequality. Octogon Mathematical Magazine, 16(1A), 275–276.
Chesneau, C. (2026). On three one-parameter families of cyclic inequalities. Journal of Computational Science and Applied Mathematics, 8(2), 207–212. https://doi.org/10.37418/jcsam.8.2.3
Chesneau, C. (2026). A collection of six two-parameter families of cyclic inequalities. Journal of Computational Science and Applied Mathematics, 8(2), 239–248. https://doi.org/10.37418/jcsam.8.2.8
Cîrtoaje, V. (2018). Mathematical inequalities -- Volume 3: Cyclic and noncyclic inequalities. Lambert Academic Publishing.
Drâmbe, M. O. (2003). Inequalities -- Ideas and methods. Ed. Gil.
Hardy, G. H., Littlewood, J. E., & Pólya, G. (1934). Inequalities. Cambridge University Press.
Lai, W.-K. (2018). Nesbitt type inequalities. International Journal of Mathematical Analysis and Applications, 6(1-B), 403–406.
Nesbitt, A. M. (1903). Problem 15114. Educational Times, 3, 37–38.
Sharma, T. P. (2023). Application of Jensen's inequality for proving Nesbitt's inequality and further generalizing it. International Journal of Scientific Research in Mathematical and Statistical Sciences, 10(2), 33–37.
Wei, F. H., & Wu, S. H. (2009). Generalizations and analogues of Nesbitt's inequality. Octogon Mathematical Magazine, 17(1), 215–220.
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