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The aim of this paper is to propose a new faster iterative method, called the MNiteration process, for approximating a fixed point of continuous functions on an arbitrary interval. Then, a necessary and sufficient condition for the convergence of the MN-iteration of continuous functions on an arbitrary interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that MN-iteration converges faster than NSP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and NSP iterations. Our findings improve corresponding results in the contemporary literature. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce new class of 2D-k-Laguerre-Konhauser polynomials, δL k,n(α,β) (x, y), which generalizes the 2D-Laguerre-Konhauser polynomials (see [18]). Then, we define a new family of bivariate k-Mittag-Leffler functions E k,α,β,δ(γ)(x, y) and establish the k-Riemann-Liouville double fractional integral and derivative of the functions E(γ) k,α,β,δ(x, y). Moreover, we introduce an integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ which contains the bivariate k-Mittag-Leffler functions E(γ) k,α,β,δ(x, y) in the kernel and investigate the semigroup property of this operator. Finally, the left inverse operator of the integral operator kε(γ) α,β,δ;ω1,ω2;a+,c+ is constructed. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of linear systems of neutral differential equations with delay. Assuming the linear parts to be given by pairwise permutable matrices, representation of a solution of a nonhomogeneous initial value problem using matrix polynomial of a degree depending on time is derived. Examples illustrating the obtained results are given. [ABSTRACT FROM AUTHOR]

A selection of ring theory papers by Jenő Szigeti is reviewed with an emphasis on aspects related to matrix algebras. [ABSTRACT FROM AUTHOR]

J. C. Robson has investigated the ideal In of all polynomials in the free associative algebra R(χ) over a non-commutative ring R generated by χ and the n² entries of an n × n matrix α = (αij), which are satisfied by . He found four cubics generating the ideal for n D 2 and proved its finite generation for any n. Ts. Rashkova has considered the ideal I2 for matrix algebras with involution over a noncommutative ring and over a field of characteristic zero. In the paper the ideal I3 is described for some special upper triangular matrices over a field of characteristic 0. The T -ideal T (U2(G)) is investigated as well for G denoting the infinite dimensional Grassmann algebra. [ABSTRACT FROM AUTHOR]