# Bulletin of the Malaysian Mathematical Sciences Society

## List of Papers (Total 17)

#### Rota–Baxter Operators on Pre-Lie Superalgebras

In this paper, we study Rota–Baxter operators and super $\mathcal {O}$-operator of associative superalgebras, Lie superalgebras, pre-Lie superalgebras and L-dendriform superalgebras. Then we give some properties of pre-Lie superalgebras constructed from associative superalgebras, Lie superalgebras and L-dendriform superalgebras. Moreover, we provide all Rota–Baxter operators of ...

#### Weak Stability of Centred Quadratic Stochastic Operators

We consider the weak convergence of iterates of so-called centred quadratic stochastic operators. These iterations allow us to study the discrete time evolution of probability distributions of vector-valued traits in populations of inbreeding or hermaphroditic species, whenever the offspring’s trait is equal to an additively perturbed arithmetic mean of the parents’ traits. It is ...

#### Moufang Loops of Odd order $p^4q^3$

It is known that all Moufang loops of order $p^4$ are associative if p is a prime greater than 3. Also, nonassociative Moufang loops of order $p^5$ (for all primes p) and $pq^3$ (for distinct odd primes p and q, with the necessary and sufficient condition $q\equiv 1({\text{ mod }}\ p)$) have been proved to exist. Consider a Moufang loop L of order $p^{\alpha }q^{\beta }$ ...

#### Functional Inequalities Involving Numerical Differentiation Formulas of Order Two

We write expressions connected with numerical differentiation formulas of order 2 in the form of Stieltjes integral, then we use Ohlin lemma and Levin–Stechkin theorem to study inequalities connected with these expressions. In particular, we present a new proof of the inequality \begin{aligned} f\left( \frac{x+y}{2}\right) \le \frac{1}{(y-x)^2} \int _x^y\int _x^yf\left( ...

#### Coronas and Domination Subdivision Number of a Graph

In this paper, for a graph G and a family of partitions $\mathcal {P}$ of vertex neighborhoods of G, we define the general corona $G \circ \mathcal {P}$ of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.

#### Diophantine Triples and k-Generalized Fibonacci Sequences

We show that if $k\ge 2$ is an integer and $\big (F_n^{(k)}\big )_{n\ge 0}$ is the sequence of k-generalized Fibonacci numbers, then there are only finitely many triples of positive integers $1<a<b<c$ such that $ab+1,~ac+1,~bc+1$ are all members of $\big \{F_n^{(k)}: n\ge 1\big \}$. This generalizes a previous result where the statement for $k=3$ was proved. The result ...

#### Vector Exponential Penalty Function Method for Nondifferentiable Multiobjective Programming Problems

In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of ...

#### Coefficient Estimates and Bloch’s Constant in Some Classes of Harmonic Mappings

Following Clunie and Sheil-Small, the class of normalized univalent harmonic mappings in the unit disk is denoted by ${\mathcal {S}}_{{\mathcal {H}}}$. The aim of the paper is to study the properties of a subclass of ${\mathcal {S}}_{{\mathcal {H}}}$, such that the analytic part is a convex function. We establish estimates of some functionals and bounds of the Bloch’s constant ...

#### Covering Problems for Functions $n$ -Fold Symmetric and Convex in the Direction of the Real Axis II

Let ${\mathcal {F}}$ denote the class of all functions univalent in the unit disk $\Delta \equiv \{\zeta \in {\mathbb {C}}\,:\,\left| \zeta \right| <1\}$ and convex in the direction of the real axis. The paper deals with the subclass ${\mathcal {F}}^{(n)}$ of these functions $f$ which satisfy the property $f(\varepsilon z)=\varepsilon f(z)$ for all $z\in \Delta$, where ...

#### A Quasistatic Electro-Viscoelastic Contact Problem with Adhesion

The aim of this paper is to study the process of contact with adhesion between a piezoelectric body and an obstacle, the so-called foundation. The material’s behavior is assumed to be electro-viscoelastic; the process is quasistatic, the contact is modeled by the Signorini condition. The adhesion process is modeled by a bonding field on the contact surface. We derive a variational ...

#### Positive Solutions for the Neumann p-Laplacian with Superdiffusive Reaction

We consider a generalized logistic equation driven by the Neumann p-Laplacian and with a reaction that exhibits a superdiffusive kind of behavior. Using variational methods based on the critical point theory, together with truncation and comparison techniques, we show that there exists a critical value $\lambda _*>0$ of the parameter, such that if $\lambda >\lambda _*$, the ...

#### Differential Subordinations and Harmonic Means

The aim of a study of the presented paper is the differential subordination involving harmonic means of the expressions $p(z)$, $p(z) + zp'(z)$, and $p(z) + \frac{zp'(z)}{p(z)}$ when $p$ is an analytic function in the unit disk, such that $p(0)=1, p(z)\not \equiv 1$. Several applications in the geometric functions theory are given.