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Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series. The bounds are procured mainly using results pertaining to theČebyšev functional. The relationship to Zeta type functions are also examined. It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.doi:10.15672/hjms.2018.579 fatcat:yvz46dhkhjfsnhxfcfwovosjpm