In this paper we provide further studies of Fenchel duality theory in the general framework locally convex topological vector (LCTV) spaces. We prove validity strong under some qualification conditions via generalized relative interiors imposed on epigraphs and domains functions involved. Our results directly generalize classical Fenchel–Rockafellar theorem from finite dimensions to LCTV

The problem of evaluating an infinite series whose successive terms are reciprocal squares the natural numbers was posed without a solution being offered in middle seventeenth century. In modern era, it is part theory Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve by considering other more tractable which were superficially similar and he hoped could be algebraica...