The irreducible Hilbert space representations of a ⁎-algebra, the graded analogue of the Lie algebra of the group of plane motions, are classified up to unitary equivalence.
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.
In this paper, we study the common fixed point and periodic point results for self-mapings in the setup of multiplicative metric spaces. We also study the well-posedness of these obtained our results. We also study the common fixed point results of mappings involved in the cyclic representation. Moreover, some applications to obtain the common solution of integral equations are presented.
The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.
On partially ordered set equipped with a partial metric, we study the sufficient conditions for existence of common fixed points of various mappings satisfying generalized weak contractive conditions. These results unify several comparable results in the existing literature.We also study the existence of nonnegative solution of implicit nonlinear integral equation. Furthermore, we study the fractal of finite family of generalized contraction mappings defined on a partial metric space.
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