Using the concepts of a pair upclass, ?-admissible and ?-subadmissible
mappings in this paper, are proven a coupled coincidence point results for
mappings F : X2 ? X and g : X ? X. In this way, recent papers [27, 33] have
been reformed and generalized. Two examples are given to support the
theoretical results. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174009]
We establish the characterisations of the classes of bounded linear operators
from the generalised Hahn sequence space hd, where d is an unbounded
monotone increasing sequence of positive real numbers, into the spaces w0, w
and w? of sequences that are strongly summable to zero, strongly summable
and strongly bounded by the Ces?ro method of order one. Furthermore, we
prove estimates for the Hausdorff measure of noncompactness of bounded linear
operators from hd into w, and identities for the Hausdorff measure of
noncompactness of bounded linear operators from hd to w0, and use these
results to characterise the classes of compact operators from hd to w and
w0. Finally, we provide an example for an application of our results.
We study a viscoelastic body involving a constitutive equation with distributed order fractional derivatives of complex order. Using a dissipation inequality in a weak form, we derive a sufficient conditions on coefficients of a model that guarantee that the Second law of thermodynamics under isothermal conditions is satisfied. Several known constitutive equations follow from our model as special cases. As an application, a new constitutive equation is related to an equation of motion of a generalized linear oscillator.
Abstract. In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015. Moreover, we give an example to support our results.
The purpose of this manuscript is to provide much simpler and shorter proofs of some recent significant results in the context of generalized F-Suzuki-contraction mappings in b-complete b-metric spaces. By using our new approach for the proof that a Picard sequence is b-Cauchy, our results generalize, complement and improve many known results in the existing literature. Further, some new contractive conditions are provided here to illustrate the usability of the obtained theoretical results.
In this paper, we first construct a b-metric, which is a special type of C * -algebra-valued b-metrics, from a given C * -algebra-valued b-metric and prove some equivalences between them. Then we show that not only fixed point results but also topological properties in C * -algebravalued b-metric spaces may be deduced from certain results in b-metric spaces. In particular, every C * -algebra-valued b-metric space is metrizable.
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