### Massimo Angrisani, Giovanni di Nella, Cinzia di Palo and Augusto Pianese

## Abstract

This paper deals with the problem of the optimal rate of return to be paid by a defined contribution pension system to its participants’ savings, namely the rate that achieves the goal of the most favorable returns on their contributions jointly with the sustainability of the pension system.

We consider defined contribution pension systems provided with a funded component, and for their study we use the “theory of the logical sustainability of pension systems” already developed in several previous works. In this paper, we focus on pension systems in a demographically stable state, whereas the productivity of the active participants and the financial rate of return on the pension system’s fund, rates that constitute the “ingredients” of the optimal rate of return on contributions, are modeled by two stochastic processes.

We show that the decisional rule defining the optimal rate of return on contributions is optimal in the sense that it is effective in terms of sustainability, and also efficient in the sense that if the system pays to its participants’ contributions a rate of return that is either higher or lower than the one provided by the rule, then the pension system becomes unsustainable or overcapitalized, respectively.

### V. A. Rukavishnikov, E. V. Matveeva and E. I. Rukavishnikova

## Abstract

We study the properties of the weighted space H^{k}
_{2α}(Ω) and weighted set W^{k}
_{2α}(Ω, δ)for boundary value problem with singularity.

### Susil Kumar Jena

## Abstract

In p. 219 of R.K. Guy's Unsolved Problems in Number Theory, 3rd edn., Springer, New York, 2004, we are asked to prove that the Diophantine equation x^{n} + y^{n} = n!z^{n} has no integer solutions with n ∈ N_{+} and n > 2. But, contrary to this expectation, we show that for n = 3, this equation has in finitely many primitive integer solutions, i.e. the solutions satisfying the condition gcd(x, y, z) = 1.

### Mustafa Saltan

## Abstract

In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterate function system (IFS). We then prove that some subgroups of p-adic numbers ℚ_{p} are strong self-similar in the sense of IFS.

### Mohammad Ashraf, Shakir Ali and Bilal Ahmad Wani

## Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δ_{n}}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δ_{n}}gn∈N is an inner *-higher derivation.

### Romi Shamoyan and Seraphim Maksakov

## Abstract

The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concern- ing zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.

### Artion Kashuri and Rozana Liko

## Abstract

In this article, we first present some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-(r; m; h)-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on m-invex set is derived. By using the notion of generalized relative semi-(r; m; h)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard, Ostrowski and Simpson type inequalities via fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

### S. Sümer Eker and Bilal Şeker

## Abstract

In this paper, defining new interesting classes, λ-pseudo bi-starlike functions with respect to symmetrical points and λ-pseudo bi-convex functions with respect to symmetrical points in the open unit disk U, we obtain upper bounds for the initial coefficients of functions belonging to these new classes.