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In this paper, we present generalized Jensen-Mercer inequality for a generalized h -convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h -convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

Let K 1 and K 2 be two one-dimensional homogeneous self-similar sets with the same ratio of contractions. Let f be a continuous function defined on an open set U ⊂ R 2 . Denote the continuous image of f by f U (K 1 , K 2) = { f (x , y) : (x , y) ∈ (K 1 × K 2) ∩ U }. In this paper we give a sufficient condition which guarantees that f U (K 1 , K 2) contains some interiors. Our result is different from Simon and Taylor's (2020, Proposition 2.9) as we do not need the condition that the product of the thickness of K 1 and K 2 is strictly greater than 1. As a consequence, we give an application to the univoque sets in the setting of q -expansions. [ABSTRACT FROM AUTHOR]

Any infinite sequence of substitutions with the same matrix of the Pisot type defines a symbolic dynamical system which is minimal. We prove that, to any such sequence, we can associate a compact set (Rauzy fractal) by projection of the stepped line associated with an element of the symbolic system on the contracting space of the matrix. We show that this Rauzy fractal depends continuously on the sequence of substitutions, and investigate some of its properties; in some cases, this construction gives a geometric model for the symbolic dynamical system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a wind speed model as a time series is presented. The main goal is to use it as a model of the load of wind turbine gears for simulation of real, varying operational conditions for wind turbine vibration modelling. Several wind characteristics for evaluation of the wind model accuracy in the context of a wind turbine gears load simulation are proposed. Verification of the hypothesis that wind speed as a time series has a fractal character is another aim of this paper. The Weierstrass functions family, whose graphs are fractal sets, in combination with medium-term trends, is used as the basis of the model. The function with a fractal component is fitted to the past observation data. A genetic algorithm is used as the fitting procedure. Fractal dimension is utilized as a parameter in a fitness function. The results have shown that the proposed approach yielded very good fit for the observation data. The hypothesis about fractal character of the wind speed is positively verified. [Copyright &y& Elsevier]