ON THE SINCOV FUNCTIONAL EQUATION
Copyright policy )ON THE SINCOV FUNCTIONAL EQUATION
The author solves the functional equation of Sincov \[ f(x,y)+f(y,z)=f(x,z) \] for mappings taking values in a semigroup satisfying the cancellation law. Then the result is applied to solve a multivalued version of the Sincov equation \[ F(x,y)+^{*} F(y,z)=F(x,z) \] where the values of \(F\) belong to \(clb(X)\) -- the family of all nonempty convex closed bounded subsets of a Banach space \(X\) and \(A+^{*}B\) denotes the closure of \(A+B\). Moreover, some results for the Riemann integral of multifunctions with values in \(clb(X)\) are obtained.
Sincov functional equation, Riemann integral, Banach space, semigroup, Functional equations for functions with more general domains and/or ranges, Set-valued set functions and measures; integration of set-valued functions; measurable selections, convex cone, multifunctions
Sincov functional equation, Riemann integral, Banach space, semigroup, Functional equations for functions with more general domains and/or ranges, Set-valued set functions and measures; integration of set-valued functions; measurable selections, convex cone, multifunctions
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