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Optimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, isdoi:10.1017/s144678870002214x fatcat:56rey74lv5ennfh6jxou7ld3de