Suppose that {Un}n≥0 is a Lucas sequence, and suppose that l1, . . . , lt are primes. We show that the equation Un1 · · ·Unm = ±l x1 1 · · · l xt t y , p prime, m < p, has only finitely many solutions. Moreover, we explain a practical method of solving these equations. For example, if {Fn}n≥0 is the Fibonacci sequence, then we solve the equation Fn1 · · ·Fnm = 2 x1 · 32 · 53 · · · 541100y under...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

The Fibonacci (p, r)-cube is an interconnection topology, which includes a wide range of connection topologies as its special cases, such as the Fibonacci cube, the postal network, etc. Klavžar and Žigert [S. Klavžar, P. Žigert, Fibonacci cubes are the resonance graphs of fibonaccenes, Fibonacci Quart. 43 (2005) 269–276] proved that Fibonacci cubes are just the Z-transformation graphs (also cal...

moslehian  and mirmostafaee, investigated the fuzzystability problems for the cauchy additive functional equation, the jensen additivefunctional equation and the cubic functional equation in fuzzybanach spaces. in this paper, we investigate thegeneralized hyers–-ulam--rassias stability of the generalizedadditive functional equation with $n$--variables, in fuzzy banachspaces. also, we will show ...

Binary sequences such as chaotic-binary (CB) sequences derived from an iterative chaotic equation have been used in selected mapping (SLM) methods to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. Though CB sequences have been shown to produce good PAPR reduction performance, their implementation requires a significant number of compl...

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost M...

In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the generalized quaternions.