On some approximate functional relations stemming from orthogonality preserving property.
In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.
In this series, this paper is devoted to the study of two related functional equations primarily connected with weighted entropy and weighted entropy of degree beta (which are weighted additive and weighted beta additive respectively) which include as special cases Shannon's entropy, inaccuracy (additive measures) and the entropy of degree beta (nonadditive) respectively. These functional equations which arise mainly from the representation and these 'additive' properties are solved for fixed m...