In such results, the involved contraction condition is considerably weakened as one is merely required to hold only on those elements which are comparable in the underlying partial ordering.
We give suitable examples to show how our results extend the well-known results of Alotaibi et al. [16], Bhaskar et al. [1] and Luong et al. [7] by significantly weakening the involved contractive condition.
In 2004, Ran and Reurings [1] extended the Banach contraction principle in ordered metric spaces for continuous monotone mappings with some applications to matrix equations wherein the involved contractive condition is required to hold merely on elements which are comparable in the underlying partial ordering.
One-factor models of CVRF clustering are pathophysiologically implausible, given the multifactorial nature of involved conditions.
Here, the involved mappings satisfy condition (a) of Theorem 2.3, and they have the unique common fixed x = 0. Remark 2.1 Theorem 2.3 generalizes and extends Theorem 1.2 of Rao and Rao [22].
Family members were informed that returning the questionnaire to the attending physician and agreeing to answer the questions about their understanding of the involved patient's condition, would constitute consent on their part.
Most of the reports examining cell death in protozoa have evaluated the involved pathways under nonphysiological conditions (physical or chemical stresses).
By studying the consequences of the involved mutations in different conditions and genetic backgrounds, the authors illustrate how knowledge of two fundamental genetic properties, pleiotropy and epistasis, may help to predict the evolution of antibiotic resistance.
This finding implies that in some growth conditions, the involved metabolic pathways are coupled in a way that a single optimal mutant is incapable to fully utilize the environment.
The existence of efficient strain communities of improved growth relative to any tested monoculture implies that in specific growth conditions, the involved metabolic pathways are coupled in a way that a single optimal mutant is incapable of fully utilizing the environment.
