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Al Qurashi, Maysaa; Rashid, Saima; Khalid, Aasma; Karaca, Yeliz; Chu, Yu-Ming

New computations of Ostrowski-type inequality pertaining to fractal style with applications. (English) Zbl 1487.26029

Fractals 29, No. 5, Article ID 2140026, 26 p. (2021).
Summary: The purpose of this paper is to provide novel estimates of Ostrowski-type inequalities in a much simpler and shorter way of some recent significant results in the context of a fractal set \(\mathbb{R}^{\tilde{\alpha}}\). By using our new approach, we established an auxiliary result that correlates with generalized convex (\(\mathcal{GC}\)) and concave functions for absolutely continuous functions with second-order local differentiable mappings. Moreover, we derived some companions of Ostrowski-type inequalities belonging to \(\mathcal{V}^{(2\tilde{\alpha})}\in L_\infty[s_1, s_2]\), \(\mathcal{V}^{(2\tilde{\alpha})}\in L_p[s_1, s_2]\) and \(\mathcal{V}^{(2\tilde{\alpha})}\in L_1[s_1, s_2]\) in local fractional sense. Our results generalize and offer better bounds than many known results in the existing literature associated with trapezoidal and midpoint formula. As an application perspective, we derived several estimation-type outcomes by the use of generalized \(\tilde{\alpha}\)-type special means formula provided here to illustrate the usability of the obtained results. Our study contributes to a better understanding of fractal analysis and proves beneficial in exploring real-world phenomena.

Cited in 10 Documents

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
28A80 Fractals

Keywords:

convex function; Ostrowski-type inequality; generalized Hölder inequality; generalized power-mean inequality; fractal sets
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References:

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