In this article, global asymptotic stability of solutions of non-homogeneous differential-operator equations of the third order is studied. It is proved that every solution of the equations decays exponentially under the Routh-Hurwitz criterion for the third order equations.
In this work, we introduce hyperbolic quaternions and their algebraic properties. Moreover, we express Euler's and De Moivre's formulas for hyperbolic quaternions.
The main goal of this study is to define a new metric space which is a generalization of complex valued metric spaces introduced by Azam et al. [1] using the set of elliptic numbers
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{\mathbb{E}_p} = \left\{ { \in = \upsilon + i\omega :\upsilon ,\omega \in \mathbb{R},\,\,{i^2} = p < 0} \right\},
and this space is named as an elliptic valued metric space. Some topological properties of this new space are examined. Also, some fixed point results are established in the setting of elliptic valued metric spaces by introducing new classes of mappings which the obtained results are real generalizations of the consequences of several fixed point theorems in the existing literature.
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