We use spectral projections of time operator in the Liouville space for simple quantum scattering systems in order to define a space of unstable particle states evolving under a contractive semi-group. This space includes purely exponentially decaying states that correspond to complex eigenvalues of this semi-group. The construction provides a probabilistic interpretation of the resonant states...

Following the definition of coupled fixed point [T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393], we prove a coupled fixed point theorem for contractive mappings in partially complete intuitionistic fuzzy normed spaces. © 2011 Elsevier Ltd. All rights reserved.

In this paper, we introduce the concept of a w-compatible mappings and utilize the same to discuss the ideas of coupled coincidence point and coupled point of coincidence for nonlinear contractive mappings in the context of complex valued metric spaces besides proving existence theorems which are following by corresponding unique coupled common fixed point theorems for such mappings. Some illus...

In this paper, we prove triple fixed point theorems in partially ordered metric spaces depended on another function. The presented results generalize the theorem of Berinde and Borcut [Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74(15) (2011) 4889–4897]. Also, we state some examples showing that our results are effective.

Probabilistic distance measures are important quantities in many research areas. For example, the Chernoff distance (or the Bhattacharyya distance as its special example) is often used to bound the Bayes error in a pattern classification task and the Kullback-Leibler (KL) distance is a key quantity in the information theory literature. However, computing these distances is a difficult task and ...

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...

In the present paper, we prove some fixed point theorems by using non-decreasing mapping \(\kappa :\mathbb{R}^+\to \mathbb{R}^+\) known as altering distance function or control function, in context of \(S\)-metric space. Further, explore property \(P\) for these contractive mappings.