In this paper we extend the notion of a Lorentz cone. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., monotone) with respect to the order defined by the cone. We determine the isotone projection sets with respect to an extended Lorentz cone. In particular a Cartesian product between an Euclidean spa...

*Correspondence: [email protected] 2Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria, 002, South Africa Full list of author information is available at the end of the article Abstract In this paper, employing a new concept of generalized compatibility of a pair of mappings defined on a product space, certain coupled coincidence point results...

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

In this paper, by reducing of coincidence and coupled fixed point results in ordered metric spaces to the respective results for mappings with one variable, some recent results established by T. G. Bhaskar and V. Lakshmikantham [T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393], V. Lakshmikantham a...

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings without mixed monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several ...

This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global pi...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand 2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok, 10400, Thailand Abstract In this paper, we establish some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having the mixed monotone property in par...

We extend the recent results of coupled coincidence point theorems of Shatanawi et. al. (2012) by weakening the concept of mixed g-monotone property. We also give an example of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by the results of Shatanawi et. al. but can be applied to our results. The main results extend and unify the results of ...

In this paper, we prove tripled fixed point theorem for nonlinear (φ,ψ)-contractive on partially ordered complete metric spaces without mixed monotone. We also prove the uniqueness of tripled fixed point of such mappings. Further, we extend the recent results of the tripled fixed point theorem of the given mapping with mixed monotone in partially orderd metric spaces.