Convexity of Solutions for an Iterative Equation in Banach Spaces

Abstract

By applying Schauder's fixed point theorem we investigate the existence of increasing (decreasing) solutions of the iterative equation H( ) ∘ = and further give conditions under which those solutions are convex or concave. As corollaries we obtain results on iterative equation ( ( ), 1 , . . . , ( )) = ( ) in Banach spaces, where 1 , 2 , . . . , ≥ 2.

On the functional equations of the q-Gamma function

“…Several general classes of functional equations have been studied [1,7,18,20,28,31]. Functional equation is one of the important concepts in mathematics and it has many applications in physics and economics [2,5,6,10,14,22,25].…”