Asian-European Journal of Mathematics

For any two right R-modules M and N, M is said to be a ps-N-injective module if, any monomorphism f : soc(N) → M can be extended to N. Also, M is called psq-injective if M is a ps-M-injective module. We discuss some properties and characterizations in terms of psq-injective modules.

An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that $|c(N(v))|\ge min\{r,d(v)\}$ for each vertex $v\in V(G)$. The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of brick product graphs.

In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators ${\breve{R}}_{n,r,s}^{(\rho ,\alpha )}(f;x)$ using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.

Let R be a non-commutative ring, and I be an ideal of R. In this paper, we generalize the definition of the zero-divisor graph of R with respect to I, and define several generalized zero-divisor graphs of R with respect to I. In this paper, we investigate the ring-theoretic properties of R and the graph-theoretic properties of all the generalized zero-divisor graphs. We study some basic properties of these generalized zero-divisor graphs related to the connectedness, the diameter and the girth. We also investigate some properties of these generalized zero-divisor graphs with respect to primal ideals.

According to Foguel, a subgroup H of a group G is called conjugate-permutable if $H{H}^x=H^{x}H$ for every $x\in G$. Mingyao Xu and Qinhai Zhang studied finite groups with every subgroup conjugate-permutable (ECP-groups) and asked three questions about them. We gave the answers to these questions. In particular, every group of exponent 3 is an ECP-group, there exist non-regular ECP-3-groups and the class of all finite ECP-groups is neither a formation nor a variety.

In this paper, we investigate permutation identities satisfied by semigroup left ideals and weak semigroup left ideals in prime nearrings. We obtain results on commutativity of multiplication and addition using these identities. We provide examples to show the necessity of certain conditions in some of the results obtained. Finally, we give a characterization of Galois field in terms of permutation identities.

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

In this paper, we study the existence and the numerical estimates of the solutions for a set of fractional differential equations. The nonlinear part of the problem, however, presupposes certain hypotheses. Particularly, for the exact localization of the parameter, the existence of a non-zero solution is established, which requires the sublinearity of the nonlinear part at origin and infinity. The novelty of this paper is to use variational methods to obtain the multiplicity of solutions of boundary value problems with the nonlinearity depending on the fractional derivative.

In this paper, we generalize the notion of expansivity, C-W expansivity and N-expansivity for impulsive dynamical systems and we prove C-W expansivity implies positive $\tau$-topological entropy. Also, we define new version of topological entropy for impulsive semiflows and we can bound this topological entropy of expansive impulsive semiflows from lower by the exponential growth rate of periodic orbits.

Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

In this paper, we give some properties of the generalized derivation algebra $GDer(T)$ of a Bihom-Lie triple system T. In particular, we prove that $GDer(T)=QDer(T)+QC(T)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that $QDer(T)$ can be embedded as derivations in a larger Bihom-Lie triple system.

The aim of this paper is to introduce Nobusawa $\mathrm{\Gamma }$-nearness hemiring theory and also to study some properties of ideals and prime (semiprime) ideals for Nobusawa $\mathrm{\Gamma }$-nearness hemirings.

Let G be an abelian group with identity e. Let R be a graded multiplicative hyperring and $\phi :E^{\mathrm{\text{gr}}}(R)\to E^{\mathrm{\text{gr}}}(R)\cup \{\varnothing \}$ be a function where $E^{\mathrm{\text{gr}}}(R)$ is the set of graded hyperideals of $R$ and $\phi (I)\subseteq I$ for every graded hyperideal I of R. In this paper, we introduce and study the concepts of graded $\phi$-2-absorbing hyperideals and graded $\phi$-2-absorbing primary hyperideals of $R$. Moreover, we give a number of main results and the basic properties concerning these classes of graded hyperideals and their homogeneous components.

This paper is the study of Hankel type translation and Hankel type convolution for linear canonical Hankel type transformations. In this paper, I have studied some inequalities associated with Hankel type translation and Hankel type convolution. Also, I have studied some applications of linear canonical Hankel transformation to a canonical convolution integral equation and a generalized nonlinear parabolic equation.

In this paper, we introduce Fibonacci backward difference operator $F{\mathrm{\Delta }}^{Bl}$ of fractional order l by the composition of Fibonacci band matrix $F$ and difference operator ${\mathrm{\Delta }}^{Bl}$ of fractional order l, defined by ${({\mathrm{\Delta }}^{Bl}x)}_s={\sum }_{i=0}^{\infty }{(-1)}^i\frac{\mathrm{\Gamma }(l+1)}{i!\mathrm{\Gamma }(l-i+1)}{x}_{s-i}$ and introduce sequence spaces ${\ell }_k(F{\mathrm{\Delta }}^{Bl})$ and ${\ell }_{\infty }(F{\mathrm{\Delta }}^{Bl}).$ We present some topological properties, obtain Schauder basis and determine $\alpha$-, $\beta$- and $\gamma$-duals of the spaces ${\ell }_k(F{\mathrm{\Delta }}^{Bl})$ and ${\ell }_{\infty }(F{\mathrm{\Delta }}^{Bl}).$ We characterize certain classes of matrix mappings from the spaces ${\ell }_k(F{\mathrm{\Delta }}^{Bl})$ and ${\ell }_{\infty }(F{\mathrm{\Delta }}^{Bl})$ to any of the space ${\ell }_{\infty },$ $c,$ $c_0$ or ${\ell }_1.$ Finally we compute necessary and sufficient conditions for a matrix operator to be compact on the spaces ${\ell }_k(F{\mathrm{\Delta }}^{Bl})$ and ${\ell }_{\infty }(F{\mathrm{\Delta }}^{Bl}).$

In this paper, we introduce a new explicit extragradient algorithm for solving Variational Inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independent of any projection onto feasible sets. Under standard and mild assumption of pseudomonotonicity and uniform continuity of the VIP associated operator, we establish the strong convergence of the scheme. Further, we apply our algorithm to find an equilibrium point with minimal environmental cost for a model in electricity production. Finally, a numerical result is presented to illustrate the given model. Our result extends, improves and unifies other related results in the literature.

This paper discusses the existence and multiplicity of positive solutions for fractional differential equations with nonlocal fractional integro-differential boundary conditions set on an unbounded domain. Using properties of Green’s function and the fixed point theory, some existence results were obtained. Three examples illustrate the existence theorems.

We introduce the Catalan transform of the Incomplete Jacobsthal numbers. We apply the Hankel transform to the Catalan transforms of these numbers. We calculate determinants of matrixes formed with $C{J}_{k,n}^l$by using Hankel transform. Then we define the incomplete h(x)-Jacobsthal polynomials. Then we examine the recurrence relation and some properties of these polynomials.

In this work, we introduce a modified inertial algorithm for solving the split common null point problem without the prior knowledge of the operator norms in Banach spaces. The strong convergence theorem of our method is proved under suitable assumptions. We apply our result to the split feasibility problem, split equilibrium problem and split minimization problem. Finally, we provide some numerical experiments including compressed sensing to illustrate the performances of the proposed method. The result presented in this paper improves and generalizes many recent important results in the literature.