Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 454093, 14 pages doi: Research Article On Approximate C∗ -Ternary m-Homomorphisms: A Fixed Point Approach M. Eshaghi Gordji,1, 2 Z. Alizadeh,1, 2 Y. J. Cho,3 and H. Khodaei1, 2 1 2 Department of Mathematics, Semnan University, . Box 35195-363, Semnan, Iran Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Semnan, Iran 3 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea Correspondence should be addressed to Y. J. Cho, yjcho@ Received 21 November 2010; Accepted 6 March 2011 Academic Editor: Jong Kim Copyright. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 454093 14 pages doi 2011 454093 Research Article On Approximate C -Ternary m-Homomorphisms A Fixed Point Approach M. Eshaghi Gordji 1 2 Z. Alizadeh 1 2 Y. J. Cho 3 and H. Khodaei1 2 1 Department of Mathematics Semnan University . Box 35195-363 Semnan Iran 2 Center of Excellence in Nonlinear Analysis and Applications CENAA Semnan University Semnan Iran 3 Department of Mathematics Education and the RINS Gyeongsang National University Chinju 660-701 Republic of Korea Correspondence should be addressed to Y. J. Cho yjcho@ Received 21 November 2010 Accepted 6 March 2011 Academic Editor Jong Kim Copyright 2011 M. Eshaghi Gordji et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Using fixed point methods we prove the stability and superstability of C -ternary additive quadratic cubic and quartic homomorphisms in C -ternary rings for the functional equation f 2x y f 2x - y m - 1 m - 2 m - 3 f y 2m-2 f x y f x - y 6f x for each m 1 2 3 4. 1. Introduction Following the terminology of 1 a nonempty set G with a ternary operation G X G X G G is called a ternary groupoid which is denoted by G . The ternary groupoid G is said to be commutative if x1 x2 x3 xơ 1 xơ 2 xơ 3 for all x1 x2 x3 e G and all permutations Ơ of 1 2 3 . If a binary operation o is defined on G such that x y z x o y o oz for all x y z e G then we say that is derived from o. We say that G is a ternary semigroup if the operation is associative that is if x y z u v x y z u v x y z u v holds for all x y z u v e G see 2 . Since it is extensively discussed in 3 the full description of a physical system S implies the knowledge of three basis ingredients the set of the observables the set of the states and the dynamics that describes the time .
