In this paper, we introduce and investigate Jensen ρ-functional inequalities associated with the following Jensen functional equationsWe prove the Hyers-Ulam-Rassias stability of the Jensen ρ-functional inequalities in complex Banach spaces and prove the Hyers-Ulam-Rassias stability of the Jensen ρ-functional equations associated with the ρ-functional inequalities in complex Banach spaces.

In this paper, we construct an additive functional equation, and use the fixed point alternative theorem to investigate the Hyers-Ulam stability of derivations fuzzy Banach space and fuzzy Lie Banach space associated with the following functional equation: f (2x − y − z)+f (x − z)+f (x + y + 2z) = f (4x).

Abstract. This paper examines the nonhomogenous Kirchhoff type equation that involves a nonlocal operator. Using Ekeland's variational principle and the Mountain pass theorem, the existence of multiple solutions is established.Mathematics subject classification (2010): 35J20, 35J60, 47G20.

We consider the Sturm-Liouville(S-L) problems with coupled boundary condition and transmission condition. Defining a Hilbert space related to the transmission conditions, we discuss the S-L problems in this modified Hilbert space. We prove the Parseval equality of the S-L problems with the transmission conditions in a modified Hilbert space and derive the Green's function for these problems.