Volume 26 (2018), Issue 1

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1. On Self-Similar Subgroups in the Sense of IFS

Mustafa Saltan.

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 ℚp are strong self-similar in the sense of IFS.

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2. On xn + yn = n!zn

Susil Kumar Jena.

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 xn + yn = n!zn 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.

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3. Nonlinear *-Lie Higher Derivations of Standard Operator Algebras

Mohammad Ashraf ; Shakir Ali ; Bilal Ahmad Wani.

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 = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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4. The Properties of the Weighted Space Hk2,α (Ω) and Weighted Set Wk2,α(Ω, δ)

V. A. Rukavishnikov ; E. V. Matveeva ; E. I. Rukavishnikova.

We study the properties of the weighted space Hk 2α(Ω) and weighted set Wk 2α(Ω, δ)for boundary value problem with singularity.

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5. Area Nevanlinna Type Classes of Analytic Functions in the Unit Disk and Related Spaces

Romi Shamoyan ; Seraphim Maksakov.

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.

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