Ranked set sampling (RSS) has been proven an efficient alternative to simple random sampling (SRS). The use of auxiliary information also helps to improve the efficiency of the estimation procedures. Therefore, to accomplish higher efficiency and discuss the optimality issues, we proffer some optimal classes of estimators under RSS by employing multi-auxiliary information. It is seen that the ordinary mean estimator, traditional regression, and ratio estimators are the subsets of the proffered estimators. The expressions of the bias and mean square error are reported. An analytical comparison under some optimality conditions points out the ascendancy of the proffered classes of estimators over all reviewed works. The theoretical results have been furnished with computational study by employing some artificial and natural populations. The computational results show that the proffered estimators outperform the conventional estimators reviewed in this study. Furthermore, apposite advices are suggested to the survey persons.
The sufficient settings of the space generated by absolute type-weighted gamma matrices of rank
p
in the Nakano complex functions of the formal power series, as well as its associated prequasioperators’ ideal equipped with definite functions, are defined and explained in this paper. Assorted prequasinorms are shown to have the Fatou characteristic. Some of its geometric and topological features and the prequasioperators’ ideal that goes with it are talked about. These structures have a relationship with the fixed points of the Kannan contraction and nonexpansive mappings. By looking at real-world examples and how they are used, it is shown that there are solutions for nonlinear dynamical systems of the Kannan type.
Consider the space of weighted binomial matrices in the Nakano sequence space of soft functions. We have offered some geometric and topological structures of the multiplication operator acting on this space and its associated operator ideal. The existence of a fixed point of the Kannan contraction operator in this prequasioperator ideal is confirmed. Finally, we discuss many applications of solutions to nonlinear stochastic dynamical matrix systems and illustrative examples of our findings.
In this paper, we construct and investigate the space of weighted Gamma matrix of order
r
in Nakano sequence space of soft functions. The idealization of the mappings has been achieved through the use of extended
s
-soft functions and this sequence space of soft functions. This new space’s topological and geometric properties, the multiplication mappings that stand in on it, and the mappings’ ideal that correspond to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated prequasi ideal. Interestingly, several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of nonlinear difference equations of soft functions are introduced.
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