We first consider a cyclic φ-contraction map on a reflexive Banach space X and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic φ-contraction maps in reflexive Banach spaces in one of their works 2009 . In the second part of the paper, we will discuss the existence of best proximity points in the framework of more gene...

The Laplacian spectral recursion, satisfied by matroid complexes and shifted complexes, expresses the eigenvalues of the combinatorial Laplacian of a simplicial complex in terms of its deletion and contraction with respect to vertex e, and the relative simplicial pair of the deletion modulo the contraction. We generalize this recursion to relative simplicial pairs, which we interpret as convex ...

A natural L∞ functional calculus for an absolutely continuous contraction is investigated. It is harmonic in the sense that for such a contraction and any bounded measurable function φ on the circle, the image can rightly be considered as φ̂(T ), where φ̂ is the solution of the Dirichlet problem for the disk with boundary values φ. The main result shows that if the functional calculus is isometri...

Very recently, Fang (Fuzzy Sets Syst. 267:86-99, 2015) gave some fixed point theorems for probabilistic φ-contractions in Menger spaces. Fang’s results improve the one of Jachymski (Nonlinear Anal. 73:2199-2203, 2010) by relaxing the restriction on the gauge function φ . In this paper, inspired by the results of Fang, we prove a new fixed point theorem for a probabilistic φ-contraction in Menge...

Cyclic weak φ-contraction mapping is introduced in Menger space and fixed point theorem for such mappings are studied in Menger space. Mathematics Subject Classification 47H10, 54H25

In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semicyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1–5]..

In this paper, we establish a common fixed point theorem for pair of quasi triangular α-orbital admissible with an interpolative (φ, ψ)- Banach-Kannan-Chatterjea type Z-contraction mappings respect to simulation function in complete metric space. An illustrative example is furnished validate our main result. Our result extends the M. S. Khan et al. [15]. As application, provide existence soluti...

In this paper, we give a generalization of Hicks type contractions and Golet type contractions in intuitionistic fuzzy metric spaces. We prove some fixed point theorems for this new type contraction mappings on intuitionistic fuzzy metric spaces. These results generalize some known results in fuzzy metric spaces and probabilistic metric spaces. AMS subject classifications: 54A40, 54E50, 54D35

In this paper, we give a generalization of Hicks type contractions and Golet type contractions on fuzzy metric spaces. We prove some fixed point theorems for this new type contraction mappings on fuzzy metric spaces.