* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract The object of this article is to determine Hyers-Ulam-Rassias stability results concerning the cubic functional equation in fuzzy normed space by using the fixed point method.

and Applied Analysis 3 Theorem 1.3 see 26–28 . Let X, d be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant L < 1. Then for each given element x ∈ X, either d ( Jx, J 1x ) ∞ 1.7 for all nonnegative integers n or there exists a positive integer n0 such that 1 d Jx, J 1x < ∞, for all n ≥ n0; 2 the sequence {Jnx} converges to a fixed p...

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnosel’skiı̆–Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed po...

* Correspondence: [email protected]. kr Department of Mathematics, Daejin University, Kyeonggi 487711, Korea Full list of author information is available at the end of the article Abstract Using fixed point method, we investigate the Hyers-Ulam stability and the superstability of partial generalized Jordan derivations on Banach modules related to Jensen type functional equations. Mathematics Subj...

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed poin...

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.

In this paper the concept of Zamfirescu single-valued maps is extend to multi-valued maps and then we study the fixed point properties. We show that the multi-valued Zamfirescu mapping has an iteration which converges to a fixed point and give a rate of convergence. Data dependence problems on multi-valued Zamfirescu mapping are studied.

In this paper, we investigate the stability problems for a functional equation f(ax + y) + af(x − y) − a2+3a 2 f(x) −a(a−1) 2 f(−x)− f(y) − af(−y) = 0 by using the fixed point method. Mathematics Subject Classification: Primary 39B82, 39B62; Secondary 47H10

Received: 09 Mar. 2012; Revised 23 Jul. 2012; Accepted 02 Sep. 2012 Received: May 8, 2012; Revised June 1, 2012; Accepted June 5, 2012 Abstract: In this paper, we’ll give some new conclusion of fixed point related to the multi-valued map, the calculation of fixed point index, and the solutions to nonlinear equations by using VIM. We apply the effective modification of its variation iteration me...