The well-known Banach’s fixed point theorem asserts that if D = X, f is contractive and (X, d) is complete, then f has a unique fixed point in X. In nonlinear analysis, the study of fixed points of given mappings satisfying certain contractive conditions in various abstract spaces has been investigated deeply. The Banach contraction principle [1] is one of the initial and crucial results in thi...

This paper is intended to consider a new approach for obtaining common fixed points under strict contractive conditions in metric spaces without assuming continuity or completeness ( or closedness) of the range of any one of the involved maps. The results proved by us can be extended to the nonexpansive or Lipschitz type mapping pairs. Our results substantially improve the results of Pant [ Dis...

For a fixed C∗-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an Adynamical system is a triple (i, B, α) where α is a ∗-endomorphism of a C∗-algebra B, and i : A ⊆ B is the inclusion of A as a C∗-subalgebra with the property that B is generated by A∪α(A)∪α(A)∪ · · · . There is a natural hierarchy in the class of A-dynamical systems, and t...

Recently Ziman et al. [3] have introduced a concept of a universal quantum homogenizer which is a quantum machine that takes as an input a system qubit initially in an arbitrary state ρ and a set of N reservoir qubits initially prepared in the same state ξ. The homogenizer realizes, in the limit sense, the transformation such that at the output each qubit is in an arbitrarily small neighbourhoo...

In 1965, Ron Douglas proved that if X is a closed subspace of an L-space and X is isometric to another L-space, then X is the range of a contractive projection on the containing L-space. In 1977 Arazy-Friedman showed that if a subspace X of C1 is isometric to another C1-space (possibly finite dimensional), then there is a contractive projection of C1 onto X. In 1993 Kirchberg proved that if a s...

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using  the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

In this paper, we shall establish some fixed point theorems for mappings with the contractive  condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work...

Fixed point and common fixed point results for generlized contractive mappings are obtianed in ordered cone metric spaces.

We provide an overview of recent results concerning the dynamics of polygonal billiards with a contractive reflection law.