The sharpening Hölder inequality via abstract convexity

Abstract

In this work, a new inequality by sharpening the well-known Hölder inequality by means of a theorem based on abstract convexity is derived.

The sharper form of a Brunn-Minkowski type inequality for boxes

“…Theorem 2.2 has been used to derive sharper versions of some inequalities in [3,19]. In a similar way, by means of this theorem, the inequality in following theorem is derived as the sharper version of the Brunn-Minkowski inequality for boxes in certain conditions.…”

“…In this paper, a Brunn-Minkowski type inequality is studied on the results based on abstract convexity which is presented [3,19]. A refinement of this inequality is derived.…”

“…have been obtained by the different authors in [1, 2, 6-15, 17, 19-22]. Also some refined or sharper versions of the well-known inequalities have been obtained by means of the results of abstract convexity in [3,16,19]. In [16], the function which is abstract convex with respect to a class of certain quadratic functions defined on R n is considered and the necessary condition for this function to have minimum on a set is expressed as an inequality involving global minimum point.…”

A refinement of the Bergström inequality

“…Many new inequalities and their versions, such as integral, fractional integral, and Hermite-Hadamard type inequalities, have been obtained for the function classes of various convexity types by different authors in [2,5,6,11,13,15,18,20,[23][24][25][26][27]. Also, sharper versions of the well-known discrete inequalities have been derived by means of the results of abstract convexity in [1,16,[20][21][22]. In [1] and [20], the sharper versions for weighted arithmetic, geometric, and harmonic mean inequalities and Hölder inequality are derived with the help of the results in [16].…”

“…Also, sharper versions of the well-known discrete inequalities have been derived by means of the results of abstract convexity in [1,16,[20][21][22]. In [1] and [20], the sharper versions for weighted arithmetic, geometric, and harmonic mean inequalities and Hölder inequality are derived with the help of the results in [16]. In this study, we give a refinement of the Bergström inequality.…”