Abstract
Based on the local fractional calculus, we establish some new generalizations of Hölder’s inequality. By using it, some related results on the generalized integral inequality in fractal space are investigated in detail.
Highlights
Let p > 1, 1/p + 1/q = 1, f(x), and g(x) be continuous real-valued functions on [a, b]
The renowned inequality of Holder [1] is well celebrated for its beauty and its wide range of important applications to real and complex analysis and functional analysis, as well as many disciplines in applied mathematics
Notice that we consider the dimensions of any fractal spaces (e.g., Cantor spaces or like-Cantor spaces) as a positive number
Summary
The renowned inequality of Holder [1] is well celebrated for its beauty and its wide range of important applications to real and complex analysis and functional analysis, as well as many disciplines in applied mathematics. The obtained results will be applied to Journal of Function Spaces and Applications establish local fractional integral reverse Minkowski inequality, Dresher’s inequality, and its corresponding reverse version.
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