### Artion Kashuri and Rozana Liko

## Abstract

In this article, we first presented a new identity concerning differentiable mappings defined on *m*-invex set via *k*-fractional integrals. By using the notion of generalized relative semi-(*r*;*m,p,q,h*
_{1},*h*
_{2})-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via *k*-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

### Bulbul Khomdram and Yumnam Rohen

## Abstract

In this paper, we prove some common coupled fixed point theorems for mapping satisfying a nonlinear contraction in *S _{b}*-metric space and some results are also given in the form of corollary. Also, some examples are given to verify the main results.

### Emine K. Sögütcü, Neşet Aydin and Öznur Gölbaşi

## Abstract

Let *R* be a ∗−prime ring with characteristic not 2, *U* a nonzero ∗− (*σ,τ*)−Lie ideal of *R*, *d* a nonzero derivation of *R*. Suppose *σ*, *τ* be two automorphisms of *R* such that *σd* = *dσ*, *τd* = *dτ* and ∗ commutes with *σ*, *τ*, *d*. In the present paper it is shown that if *d*(*U*) ⊆ *Z* or *d*
^{2}(*U*) ⊆ *Z*, then *U* ⊆ *Z*.

### B. Usna Banu and G. P. Youvaraj

## Abstract

In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on 𝔻 = {*z* ∈ ℂ: |*z*| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of *n ^{th}* sections have been obtained.

### 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.

### Włodzimierz Łenski and Bogdan Szal

## Abstract

We extend and improve the some results of Xh. Z. Krasniqi [Int. J. of Anal. and Appl. Vol. 1, 33-39 (2013)], M. L. Mittal and M. V. Singh [Operators, Int. J. of Analysis, Vol. 2015, Article ID 478345, 4 pages] and from many other papers on summability of Fourier-Laguerre series to strong summability proving the estimate of the deviation of the partial sums from considered functions. There also is a remark on summability methods used in cited papers.

### S. H. Saker, D. M. Abdou and I. Kubiaczyk

## Abstract

In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale 𝕋. We will derive the integral and discrete inequalities of Pólya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

### 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.