The strong normal system of some compact right topological groups

The aim of the present paper is to characterize the strong normal system of the Ellis groups of a well-known family of dynamical systems on the finite and infinite dimensional tori.

Boundary value problems for Hilfer fractional differential equations with Katugampola fractional integral and anti-periodic conditions

The purpose of this paper is to investigate the existence and uniqueness of solutions for a new class of nonlinear fractional differential equations involving Hilfer fractional operator with fractional integral boundary conditions. Our analysis relies on classical fixed point theorems and the Boyd-Wong nonlinear contraction. At the end, an illustrative example is presented. The boundary conditions introduced in this work are of quite general nature and can be reduce to many special cases by fixing the parameters involved in the conditions.

On a second-order differential inclusion with certain integral and multi-strip boundary conditions

We study a second-order differential inclusion with integral and multi-strip boundary conditions defined by a set-valued map with nonconvex values. We obtain an existence result and we prove the arcwise connectedness of the solution set of the considered problem.

Some new inequalities for convex functions via generalized integral operators and their applications

The authors discover an identity for a generalized integral operator via differentiable function. By using this integral equation, we derive some new bounds on Hermite–Hadamard type integral inequality for differentiable mappings that are in absolute value at certain powers convex. Our results include several new and known results as particular cases. At the end, some applications of presented results for special means and error estimates for the mixed trapezium and midpoint formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the field of integral inequalities.

Differential identities in prime rings

Let R be a prime ring with center Z(R) and alpha,beta be automorphisms of R. This paper is divided into two parts. The first tackles the notions of (generalized) skew derivations on R, as the subject of the present study, several characterization theorems concerning commutativity of prime rings are obtained and an example proving the necessity of the primeness hypothesis of R is given. The second part of the paper tackles the notions of symmetric Jordan bi (alpha,beta)-derivations. In addition, the researchers illustrated that for a prime ring with char(R) different from 2, every symmetric Jordan bi (alpha,alpha)-derivation D of R is a symmetric bi (alpha,alpha)-derivation.

A note on the Diophantine Equation x^2-kxy+ky^2+ly=0

We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.

A study of some forms of continuity for multifunctions in ideal topological spaces

The main goal of this article is to introduce the concepts of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions. Some characterizations of *(alpha)-continuous multifunctions and almost *(alpha)-continuous multifunctions are established. Furthermore, the relationships between *(alpha)-continuity and almost *(alpha)-continuity are discussed.

Uniqueness and existence of solutions for nonlinear fractional differential equations with two fractional orders

We study the existence and uniqueness of solutions for integro-differential equations involving two fractional orders. By using the Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence and uniqueness of solutions are obtained. Some illustrative examples are also presented.

Some perturbed inequalities of Ostrowski type for twice differentiable functions

We establish new perturbed Ostrowski type inequalities for functions whose second derivatives are of bounded variation. In addition, we obtain some integral inequalities for absolutely continuous mappings. Finally, some inequalities related to Lipschitzian derivatives are given.

A generalization of weighted bilinear Hardy inequality

In this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using certain weighted mean operators.