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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]

In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials. [ABSTRACT FROM AUTHOR]

In this paper, by the differential operator we give some congruences and new proof for some known congruence concerning the Bell polynomials, derangement polynomials and r-Lah polynomials. [ABSTRACT FROM AUTHOR]