Gronwall, Bihari and Langenhop type inequalities for discrete Pfaffian equation (Q1262475)

The author establishes upper and lower bounds on the module of a solution of discrete Pfaffian equation in two independent variables \[ x(t_ 1,t_ 2)=x(0,0)+\sum^{t_ 1-1}_{s_ 1=0}f_ 1(s_ 1,t_ 2,x(s_ 1,t_ 2))+\sum^{t_ 2-1}_{s_ 2=0}f_ 2(0,s_ 2,x(0,s_ 2)) \] where \(x:{\mathbb{N}}\times {\mathbb{N}}\to {\mathbb{R}}\) and \(f_ i:{\mathbb{N}}\times {\mathbb{N}}\times {\mathbb{R}}\to {\mathbb{R}},\) \(i=1,2\).