Asian-European Journal of Mathematics

In this paper, a new class of analytic functions is introduced on the unit disk U which is defined by a certain differential operator. Some inclusion properties are discussed. Indeed, three other classes are also introduced and some differential subordination results are obtained.

The structure of a completely π-regular semigroup with 0-modular or 0-distributive subsemigroup lattice is given. Furthermore, it is shown that an eventually inverse semigroup to have 0-modular or 0-distributive subsemigroup lattice is a completely π-regular semigroup which is a semilattice of completely archimedean semigroups. Thus the structure of an eventually inverse semigroup whose subsemigroup lattice is 0-modular or 0-distributive is characterized as well.

In Kleinfeld [Assosymmetric rings, Proc. Amer. Math. Soc.8 (1957) 983–986] showed that every commutator and every associator is in the nucleus N. In this paper, first we prove that the nucleus coincides with the center of the ring. Using this result and results of Kleinfeld, it is shown that a simple assosymmetric ring is third power associative and hence associative.

In this paper, we investigate generalized derivations satisfying certain differential identities on semigroup ideals of right near-rings and discuss related results. Moreover, we provide examples to show that the assumed restrictions cannot be relaxed.

In the present paper, we introduce the notion of (σ, τ)-n-derivation in near-ring N and investigate some properties involving (σ, τ)-n-derivations of a prime near-ring N which force N to be a commutative ring. Additive commutativity of near-ring N satisfying certain identities involving (σ, τ)-n-derivations of a prime near-ring N has also been obtained. Related examples to justify the hypotheses in various theorems have also been provided.

In this study, we introduce the concepts of pointwise λ-statistical convergence of order α and pointwise [V, λ]-summability of order α of sequences of real valued functions. Some relations between -statistical convergence and strong -summability are given.

In this paper, we employ the idea of exclusion of a condition given by Shahzad and Zegeye [on Mann and Ishikawa iteration schemes for multivalued maps in Banach spaces, Nonlinear Anal. Theory Methods Appl.71(3–4) (2009) 838–844] to our iterative process which converges much faster than Mann, Ishikawa and Agarwal's iterative processes.

The aim of this paper is to use higher-order energy balance method as a novel solution procedure for investigation the nonlinear oscillation of various systems. The method is associated with collocation method and employed for a group of nonlinear problems including pure cubic nonlinearity, fractional elastic force and duffing harmonic terms. Obtained results are evaluated by comparing with the classical balance method and also the exact solutions computed numerically. It is shown our solution procedure achieves more accurate results versus the classical solution and higher agreement are observed between the newer solutions and the exact ones for the systems. Effect of initial conditions in the nonlinear natural frequencies are carried out for a range of small and large values and it is proved the proposed method is not only simple but also more reliable for analysis of such systems.

One of the most common way to generate a fractal is by using an iterated function system (IFS). In this paper, we introduce an (n, m)-IFS, which is a collection of n IFSs and discuss the attractor of this system. Also we prove the continuity theorem and collage theorem for (n, m)-IFS.

Here, being motivated from the works of Zhu, Guo and Shum on left Clifford semigroups, we have introduced left k-Clifford semirings as a generalization of k-Clifford semirings. A k-regular semiring S ∈ 𝕊𝕃⁺ is a left k-Clifford semiring (left k-semifield) if for all a ∈ S, (for all b ∈ S′, ). Several characteristics for this class of semirings are obtained. Moreover a semiring is left k-Clifford if and only if it is a distributive lattice of left k-semifields.

The main difficulty in solving nonlinear differential equations by the differential transformation method (DTM) is how to treat complex nonlinear terms. This method can be easily applied to simple nonlinearities, e.g. polynomials, however obstacles exist for treating complex nonlinearities. In the latter case, a technique has been recently proposed to overcome this difficulty, which is based on obtaining a differential equation satisfied by this nonlinear term and then applying the DTM to this obtained differential equation. Accordingly, if a differential equation has n-nonlinear terms, then this technique must be separately repeated for each nonlinear term, i.e. n-times, consequently a system of n-recursive relations is required. This significantly increases the computational budget. We instead propose a general symbolic formula to treat any analytic nonlinearity. The new formula can be easily applied when compared with the only other available technique. We also show that this formula has the same mathematical structure as the Adomian polynomials but with constants instead of variable components. Several nonlinear ordinary differential equations are solved to demonstrate the reliability and efficiency of the improved DTM method, which increases its applicability.

In this paper, an implicit finite-difference method is proposed for the numerical solutions of one-dimensional coupled nonlinear Burgers' equations on the uniform grid. The proposed Crank–Nicolson scheme forms a system of nonlinear difference equations which has to be solved at each iteration. The nonlinear assembled system of equations has been linearized by applying Newton's iteration method. The obtained linear system has been solved by using Gauss elimination with partial pivoting method. Three numerical examples have been given in order to demonstrate the accuracy and efficiency of the proposed scheme. Computed results have been compared well with the analytical solutions and those already available in the literature via the error norms.

By the use of the celebrated Kato's inequality we obtain in this paper some inequalities for operator-valued integrals on a complex Hilbert space H. Among others, we show that

The concepts of annulets and α-ideals are introduced in C-algebras. α-ideals are characterized in terms of annulets and minimal prime ideals. A set of equivalent conditions is established for every ideal of a C-algebra to become an α-ideal. Some topological properties of the class of all prime α-ideals are studied in a C-algebra.

Many rings and algebras arising in quantum mechanics can be interpreted as skew Poincaré–Birkhoff–Witt (PBW) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others, are examples of skew PBW extensions. In this paper, we extend the classical Ore and Goldie theorems, known for skew polynomial rings, to this wide class of non-commutative rings. As application, we prove the quantum version of the Gelfand–Kirillov conjecture for the skew quantum polynomials.

This paper classifies the Vogan diagram of the untwisted affine Kac–Moody superalgebras.