Asian-European Journal of Mathematics

The objective of this paper is to obtain an upper bound to the second Hankel determinant for the functions belonging to strongly starlike and convex functions of order α(0 < α ≤ 1). Further, we introduce a subclass of analytic functions and obtain the same coefficient inequality for the functions in this class, using Toeplitz determinants.

In this paper, we establish coupled coincidence point results in probabilistic metric spaces with a partial order. The main theorem has several corollaries and is supported with an example. The corollaries are shown to be properly contained in the main theorem. By an application of a corollary we obtained a corresponding result in metric spaces which is also supported with an example. Some results in [Nonlinear Anal. 74 (2011) 6451–6458] and [Nonlinear Anal. 71 (2009) 1833–1843] are extended in this paper. The extensions are shown to be actual with the help of an example. We use Hadžić type t-norm in this paper. The methodology of the proofs in this work is a blending of analytic and order theoretic approaches.

We obtain nth-order q-derivatives of certain multivariable q-hypergeometric series with respect to parameters. We consider fourteen 3-variable q-Lauricella series, four k-variable q-Lauricella series and the generalized q-Kampé de Fériet series for this purpose. Some relations between q-derivatives of these series with respect to parameters and variables are also given.

Characterized Quasi-complemented Almost Distributive Lattice (ADL) in terms of dominator ideals. By using the closure operator on the set of all ideals of an ADL introduced the concept of closure ideals and studied their important results. Finally, the class of all closure ideals of ADL are isomorphic to the class of all ideals of .

In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.

Let n be a positive integer, σ be an element of the symmetric group and let σ be a cycle of length n. The elements are σ-equivalent, if there are natural numbers k and l, such that σ^k α = βσ^l, which is the same as the condition to exist natural numbers k₁ and l₁, such that α = σ^k₁ βσ^l₁. In this work, we examine some properties of the so-defined equivalence relation. We build a finite oriented graph Γ_n with the help of which is described an algorithm for solving the combinatorial problem for finding the number of equivalence classes according to this relation.

A corrector–predictor algorithm is proposed for solving semidefinite optimization problems. In each two steps, the algorithm uses the Nesterov–Todd directions. The algorithm produces a sequence of iterates in a neighborhood of the central path based on a new proximity measure. The predictor step uses line search schemes requiring the reduction of the duality gap, while the corrector step is used to restore the iterates to the neighborhood of the central path. Finally, the algorithm has iteration complexity.

In this paper, we investigate a boundary problem with nonlocal conditions for mixed parabolic–hyperbolic type equation with three lines of type changing. Considered domain contains a rectangle as a parabolic part and three domains bounded by smooth curves and type-changing lines as a hyperbolic part of the mixed domain. Applying method of energy integrals we prove the uniqueness of the solution for the considered problem. The proof of the existence will be done by reducing the original problem into the system of the second kind Volterra integral equations.

We use a rank-based measure on rational expressions in indeterminates over a field and define notions of size and depth with associated subparts of formulae for expressions. Formulae are allowed to have as inputs expressions from a large set rather than just constants and indeterminates. A general lower bound is derived and this is used to deduce an exponential lower bound, subject to depth assumptions, on the formula size of the determinant with inputs restricted to the usual constants and indeterminates. The general bound is also used to show that a polynomial which is closely related to the determinant has exponential formula size if either (i) some types of operations do not occur in the formula or (ii) some assumptions on depth hold (the inputs allowed here are from a large set).

In queueing systems with multi-server models, every server goes on vacation irrespective of the availability of the server in the system. This creates inconvenience to the customers in places like computer network, communication network, hospitals, telegraph offices and telephone booths, etc., where at least one server must be available in the system for service. In this paper, an analysis has been carried out on a bulk service queueing system with two servers in which at least one server is available for service in the system always.

In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner–Shirshov bases and linear bases of free commutative Rota–Baxter algebra, free commutative λ-differential algebra and free commutative λ-differential Rota–Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative Ω-words.

Let be a generalized dihedral group of order 2n and 𝔽_q be a finite field having q elements. In this note, we establish the structure of the unit group of for any odd n ≥ 3. This extends a result due to Kaur and Khan [Units in 𝔽₂D_2p, J. Algebra Appl. 13(2) (2014) 9pp., doi: 10.1142/S0219498813500904] as well as a result due to the authors [Units in 𝔽_2^kD_2n, Int. J. Group Theory 3(3) (2014) 25–34].