GLORIA — GEOMAR Library Ocean Research Information Access

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New theta-function identities and general theorems for the explicit evaluations of Ramanujan’s continued fractions (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-08-03

Description: We prove some new theta-function identities for two continued fractions of Ramanujan which are analogous to those of Ramanujan–Göllnitz–Gordon continued fraction. Then these identities are used to prove new general theorems for the explicit evaluations of the continued fractions.

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Topics: Mathematics

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Solvability of impulsive periodic boundary value problems for higher order fractional differential equations (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-08-03

Description: A class of periodic boundary value problems for higher order fractional differential equations with impulse effects is considered. We first convert the problem to an equivalent integral equation. Then, using a fixed-point theorem in Banach space, we establish existence results of solutions for this kind of boundary value problem for impulsive singular higher order fractional differential equations. Two examples are presented to illustrate the efficiency of the results obtained.

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Topics: Mathematics

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On Durrmeyer-type generalization of ( p , q )-Bernstein operators (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-08-03

Description: In this paper, we introduce ( p , q )-Bernstein Durrmeyer operators. We define ( p , q )-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin’s theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K -functional. Finally, we find Voronovskaya-type theorem for the operators.

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Topics: Mathematics

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Approximation of functions by de la Vallée-Poussin sums in weighted Orlicz spaces (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-06-28

Description: We investigate problems of estimating the deviation of functions from their de la Vallée-Poussin sums in weighted Orlicz spaces L M ( T, ω ) in terms of the best approximation ${E_{n}(f)_{M, \, \omega }}$ .

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Topics: Mathematics

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Radial basis function networks for delay differential equation (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-05-09

Description: In this article, a numerical technique is developed for solving delay differential equations. The proposed method combines the method of steps with the radial basis function networks. A delay differential equation is transformed to an ordinary differential equation and then the radial basis function collocationmethod is implemented to find the solution of the ordinary differential equation. The procedure for implementation of the radial basis function collocation method and the proposed method for delay differential equation is presented in detail. Numerical experiments are carried out on a number of examples to show the advantages of the proposed technique over the radial basis function collocation method.

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Topics: Mathematics

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Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-04-07

Description: In this paper, we introduce and study a new class of CR-lightlike submanifold of an indefinite nearly Sasakian manifold, called quasi generalized Cauchy–Riemann (QGCR) lightlike submanifold. We give some characterization theorems for the existence of QGCR-lightlike submanifolds and finally derive necessary and sufficient conditions for some distributions to be integrable.

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Topics: Mathematics

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Application of operational matrices to numerical solution of stochastic SIR model (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-02-21

Description: The goal of this paper is to give useful method for solving a problem in biologic system that is formulated by stochastic Volterra integral equations. Here, we consider triangular functions, block pulse functions and their operational matrices of integration. Illustrative example is included to demonstrate the validity and applicability of the operational matrices.

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Topics: Mathematics

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On multiple Walsh–Fourier coefficients of functions of $${{\phi-\Lambda}}$$ ϕ - Λ -bounded variation (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-02-17

Description: Here, we have estimated the order of magnitude of multiple Walsh–Fourier coefficients of functions of ${\phi(\Lambda^1,\ldots,\Lambda^N)BV([0,1]^{N})}$ .

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Topics: Mathematics

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A note on isomorphism theorems of Krasner ( m , n )-hyperrings (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-01-23

Description: Recently, Krasner ( m , n )-hyperrings were introduced and analyzed by Davvaz et. al. This is a suitable generalization of Krasner hyperrings. In this research work, we consider that if I is a normal hyperideal of a Krasner ( m , n )-hyperring R , then the quotient hyperring [ R : I *] is an ( m , n )-ring. Moreover, we prove that if R is a multiplicative ( m , n )-ary hyperring and I is a normal hyperideal of R , then [ R : I *] is an ( m , n )-ring.

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Topics: Mathematics

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Ulam stabilities for partial Hadamard fractional integral equations (2016)

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In: Arabian Journal of Mathematics

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Publication Date: 2016-01-13

Description: This paper deals with some existence and Ulam stability results for a class of partial integral equations via Hadamard’s fractional integral, by applying Schauder’s fixed-point theorem.

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Topics: Mathematics

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