FIXED POINT THEOREM AND A UNIQUENESS THEOREM CONCERNING THE STABILITY OF FUNCTIONAL QUATIONS IN MODULAR SPACES

摘要

In this paper, we investigate a fixed point theorem in modular spaces, whose induced modular is lower semi-continunous, for a mapping with some conditions in place of the condition of bounded orbit. Using this fixed point theorem, we prove the generalized Hyers-Ulam stability for the following additive-quadratic functional equation f(2x + y) + f(2x y) 2f(x + y) 2f(x y) 2f(2x) + 4f(x) = 0 in modular spaces.