We present various kinds of statistical convergence and I-convergence for sequences of functions with values in 2-normed spaces and obtain a criterion for I-convergence of sequences of functions in 2-normed spaces. We also define the notion of I-equistatistically convergence and study I-equistatistically convergence of sequences of functions.

Abstract. Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.

Let D be a derivation on a Banach algebra; by using the operator D2, we give necessary and sufficient conditions for the separating ideal of D to be nilpotent. We also introduce an ideal M(D) and apply it to find out more equivalent conditions for the continuity of D and for nilpotency of its separating ideal

We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert -Schmidt norm of matrices. We give a uniformly and abbreviated form of the inequalities presented by Kittaneh and Mansarah, and the inequalities presented by Kai and we obtain some of their operator and matrix versions.

Abstract. In this paper, we investigate Jordan homomorphisms in proper JCQ * -triples associated with the generalized 3-variable Jesnsen functional equationwith r ∈ (0, 3) \ {1}. We moreover prove the Hyers-Ulam-Rassias stability of Jordan homomorphisms in proper JCQ * -triples.