Recently, Wardowski introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, in this paper, we ...will present some fixed point results of Hardy-Rogers-type for self-mappings on complete metric spaces or complete ordered metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.
This article reviews the recent advances in the uniqueness and multiplicity of competitive equilibria in models arising in mathematical economics, finance, macroeconomics, and trade.
Opinion leaders are important sources of advice for other consumers. Instagram is the most used platform by opinion leaders in the fashion industry, and this trend is expected to continue in the near ...future. This study aims to identify some key antecedents and consequences of opinion leadership in this context. Our results, based on data collected from 808 followers of a fashion focused Instagram account, suggest that originality and uniqueness are crucial factors if a user is to be perceived as an opinion leader on Instagram. In addition, opinion leadership influences consumer behavioral intentions toward both the influencer (intention to interact in the account and recommend it) and the fashion industry (intention to follow fashion advice posted). Finally, the perceived fit of the account with the consumer's personality strengthens the influence of opinion leadership on the intention to follow published advice. These results have interesting implications for the fashion industry.
•Data from 808 followers of an Instagram account focused on fashion is analyzed.•Originality and uniqueness positively influence opinion leadership on Instagram.•Opinion leadership affects consumers' intention to follow the influencer's advice.•Opinion leadership affects behavioral intentions related to the influencer.•Perceived fit and online interaction propensity act as moderators.
This paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two ...impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of \(\gamma\) in the HARA utility function \(\frac{\gamma}{1-\gamma}\left(b+\frac{a}{\gamma}x\right)^{1-\gamma}\). The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in 4.
Canonical Polyadic Decomposition (CPD) of a third-order tensor is a minimal decomposition into a sum of rank-1 tensors. We find new mild deterministic conditions for the uniqueness of individual ...rank-1 tensors in CPD and present an algorithm to recover them. We call the algorithm “algebraic” because it relies only on standard linear algebra. It does not involve more advanced procedures than the computation of the null space of a matrix and eigen/singular value decomposition. Simulations indicate that the new conditions for uniqueness and the working assumptions for the algorithm hold for a randomly generated I×J×K tensor of rank R≥K≥J≥I≥2 if R is bounded as R≤(I+J+K−2)/2+(K−(I−J)2+4K)/2 at least for the dimensions that we have tested. This improves upon the famous Kruskal bound for uniqueness R≤(I+J+K−2)/2 as soon as I≥3.
In the particular case R=K, the new bound above is equivalent to the bound R≤(I−1)(J−1) which is known to be necessary and sufficient for the generic uniqueness of the CPD. An existing algebraic algorithm (based on simultaneous diagonalization of a set of matrices) computes the CPD under the more restrictive constraint R(R−1)≤I(I−1)J(J−1)/2 (implying that R<(J−12)(I−12)/2+1). We give an example of a low-dimensional but high-rank CPD that cannot be found by optimization-based algorithms in a reasonable amount of time while our approach takes less than a second. We demonstrate that, at least for R≤24, our algorithm can recover the rank-1 tensors in the CPD up to R≤(I−1)(J−1).
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