* Correspondence: [email protected] Department of Mathematics Education, College of Education, Mokwon University, Daejeon, 302729, Korea Full list of author information is available at the end of the article Abstract Using the fixed-point method, we prove the generalized Hyers-Ulam stability of the functional equation f (x + y, z + w) + f (x− y, z− w) = 2f (x, z) + 2f (y,w). The quadratic for...

Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of a functional equation of the square root spiral, f (√ r2 + 1 ) = f(r)+ tan−1(1/r).

Received: 27 March 2012; Accepted: 25 July 2012. Published online: XX July. 2012 Abstract: In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continui...

The aim of this paper is to present a common fixed point theorem in a metric space which extends the result of P.C.Lohani & V.H.Bhadshah using the weaker conditions such as Reciprocally continuous, Compatible mappings, Weakly compatible and Associated sequence.

In this paper, we mainly prove a coincidence theorem and common fixed point theorem in M-fuzzy metric spaces which improve the results of Som [11] who proved his results on Metric and Banach spaces. Also we improve and extend some known results of Veerapandi et al. [12] by extending three mappings to four weak compatible mappings. Mathematics Subject Classification: 47H10, 54H25.

In this article, we study the controllability of impulsive functional differential equations with nonlocal conditions. We establish sufficient conditions for controllability, via the measure of noncompactness and Mönch fixed point theorem.

The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...

In this paper we extend some existing results and prove fixed point theorem on partially ordered cone metric spaces which satisfy certain weak contractive inequalities. In this consequence we have also given some illustrative examples.

In this paper, we prove some common fixed point theorems for two pair of compatible and subsequentially continuous mappings satisfying an implicit relation in Modified Intuitionistic fuzzy metric spaces. Consequently, our results improve and sharpen many known common fixed point theorems available in the existing literature of metric fixed point theory.

In 1994, S.G. Matthews introduced the notion of a partial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill generalized Matthews’ notion of partial metric, in order to establish connections between these structures and the topological aspects of domain theory. Here, we obtain a Banach fixed point theorem for complete partial me...