Some orthogonality equation with two functions

A functional equation with two unknown functions

Some topics in orthogonality

Equation with residuated functions

The structure of solution-sets for the equation F (x) = G(y) is discussed, where F, G are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of x, y. Properties are defined which are sufficient for finite termination. The particular cas...

Approximation solution of two-dimensional linear stochastic Volterra-Fredholm integral equation via two-dimensional Block-pulse ‎functions

In this paper, a numerical efficient method based on two-dimensional block-pulse functions (BPFs) is proposed to approximate a solution of the two-dimensional linear stochastic Volterra-Fredholm integral equation. Finally the accuracy of this method will be shown by an example.

Superstability of the generalized orthogonality equation on restricted domains

Chmieliński has proved in the paper [4] the superstability of the generalized orthogonality equation |〈 f (x), f (y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmieliński by proving a theorem: Let Dn be a suitable subset of Rn. If a function f : Dn → Rn satisfies the inequality ||〈 f (x), f (y)〉|− |〈x,y〉|| ≤ φ(x,y) for an appropriate control function φ(x,y) and for all x,y ∈ Dn, ...