Journal of Mathematical Extension
Volume:9 Issue: 3, Summer 2015

In this paper, we consider the Hyers-Ulam-Rassias stability of the following equation f(x) = af(h(x)) + bf(−h(x)) in the fuzzy normed spaces with some conditions imposed on the constants a, b and the function h on a nonempty set X.

Fuzzy distance measure is one of the most useful tools in applications. Many distance methods have been proposed so far. However, there is no method that can always give a satisfactory solution to every situation. In this paper, we propose a new algorithm to determine distance between two fuzzy numbers. The proposed method could be developed in n-dimentions. Finally, some numerical examples demonstrate the advantages of this method.

This paper deals with a construction of both stationary and non-stationary M-band tight framelet packets in L2(R) using extension principles. The approach here is different from the method described by Shah and Debnath in [ Explicit construction of M-band tight framelet packets, Analysis, 32 (2012) 281-294 ] in that we directly decompose the multiresolution space VJ for a fixed level J > 0 to the level 0 with any combined wavelet mask m = [m0,m1, . . . ,mL] satisfying the unitary extension principle condition M()M() = IM, where M() =  m` 􀀀  + 2p M
M−1 `,p=0.

This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations.

Let G be a simple graph of order n. The energy E(G) of G is the sum of the absolute values of the eigenvalues of G. The Randi´c matrix of G, denoted by R(G), is defined as the n×n matrix whose (i, j)- entry is (didj ) −1 2 if vi and vj are adjacent and 0 for another cases. The Randi´c energy RE(G) of G is the sum of absolute values of the eigenvalues of R(G). In this paper we compute the energy and the Randi´c energy for certain graphs. We also propose a conjecture on the Randi´c energy.

In this paper, we introduce a new type of iterated function systems, named; CIFS. Actually in a CIFS we have some flows instead of some functions in iterated function systems. Then, we generalize the notions of average shadowing property, chain transitivity, and attractor sets on a CIFS. It is shown that every uniformly contracting CIFS has the average shadowing property. We also prove that if a CIFS, F on a compact metric space X has the average shadowing property, then F is chain transitive, but the converse is not always true. As a result, this proves that if F is an uniformly contracting CIFS on compact metric space X, then X is the only nonempty attractor of F.

Decomposer functions in algebraic structures are studied in many recent papers. They have close relations to factorization by two subsets. Also, idempotent endomorphisms form a class of (strong) decomposer functions in groups. Now, if the algebraic structure is a group, then by introducing a type of local homomorphisms we obtain several properties and equivalent conditions for many classes of decomposer functions and get a new result regarding to factorization of a group by its two subsets. Moreover, we prove existence of (two-sided) decomposer type functions in non-simple groups.

The Generalized Minimal Residual method (GMRES) is often used to solve a large and sparse system Ax = b. This paper establishes error bound for residuals of GMRES on solving an N × N normal tridiagonal Toeplitz linear system. This problem has been studied previously by Li [R.-C. Li, Convergence of CG and GMRES on a tridiagonal Toeplitz linear system, BIT 47 (3) (2007) 577-599.], for two special right-hand sides b = e1 , eN . Also, Li and Zhang [R.-C. Li, W. Zhang, The rate of convergence of GMRES on a tridiagonal Toeplitz linear system, Numer. Math. 112 (2009) 267-293.] for non-symmetric matrix A, presented upper bound for GMRES residuals. But in this paper we establish the upper bound on normal tridiagonal Toeplitz linear systems for special right-hand sides b = b(l)el, for 1  l  N .