Refinement of Hölder inequality and application to Ostrowski inequality

Pure and Applied Mathematics

“…we have the inequality In [106], we can …nd the following theorem: Then The main aim of this section is to develop an Ostrowski type inequality for random variables whose probability density functions are in L p [a; b] based on (7.25).…”

Local Fractional Integral Hölder-Type Inequalities and Some Related Results

“…The above two inequalities play an important role not only in pure mathematics but also in applied mathematics. A variety of generalizations and refinements have been studied in the literature; the reader can be referred to [3][4][5][6][7][8][9][10][11][12] and the cited references therein.…”

Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space

“…Both the Cauchy inequality and the Hölder inequality play significant roles in many different branches of modern pure and applied mathematics. A great number of generalizations, refinements, variations, and applications of each of these inequalities have been studied in the literature (see [3][4][5][6][7][8][9][10][11][12][13] and the references cited therein). Recently, Yang [14] established the following local fractional integral Hölder's inequality on fractal space.…”

“…The purpose of this paper is to give some new generalizations and refinements of inequalities (6) and (7). Some related inequalities are also considered.…”

“…Remark 9. Upon setting = , = −1/ , for ̸ = , and = 1 − 1/ , inequalities (24) and (25) are reduced to inequalities (6) and 7, respectively.…”