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Abstract. The concept of I -convergence is a generalization of statistical convergence and it is depended on the notion of the ideal I of subsets of the set N of positive integers. In this paper for sequences in 2 -normed space the relationship between I -convergence and usual convergence along a filter F (I ) associated with an admissible ideal I with property (AP) is investigated. We introduce the concepts I -Cauchy and I * -Cauchy sequences in 2 -normed spaces and study their certain properties.Mathematics subject classification (2000): 40A05, 46A70, 40A99, 46A99.

ABSTRACT:In this paper, we introduce the notion of -[V, λ]-summability and -λ-statistical convergence with respect to the intuitionistic fuzzy norm (µ, v), investigate their relationship, and make some observations about these classes. We mainly examine the relation between these two new methods and the relation between -λ-statistical convergence and -statistical convergence in the corresponding intuitionistic fuzzy normed space.

Abstract. We give operator analogues of some classical inequalities, including Hardy and HardyHilbert type inequalities for numbers. We apply these operator forms of such inequalities for proving some power inequalities for the so-called Berezin number of self-adjoint and positive operators acting on Reproducing Kernel Hilbert Spaces (RKHSs). More precisely, we prove thatfor some constants C > 1. We also use reproducing kernels technique to estimate dist (A,U ) , where U is the set of all unitary operators on a RKHS H = H (Ω) over some set Ω, for some operator A on H (Ω) .Mathematics subject classification (2010): 47A63.

By using Hardy-Hilbert's inequality, some power inequalities for the Berezin number of a selfadjoint operators in Reproducing Kernel Hilbert Spaces (RKHSs) with applications for convex functions are given.

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In the present paper we are concerned with I-convergence of sequences of functions in random 2-normed spaces. Particularly, following the line of recent work of Karakaya et al. [23], we introduce the concepts of ideal uniform convergence and ideal pointwise convergence in the topology induced by random 2-normed spaces, and give some basic properties of these concepts.

We introduce the notions of lacunary -convergence and lacunary -Cauchy in the topology induced by random -normed spaces and prove some important results.