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. 2024 Nov 27;10(23):e40664.
doi: 10.1016/j.heliyon.2024.e40664. eCollection 2024 Dec 15.

Novel versions of Hölder's-Like and related inequalities with newly defined L P space, and their applications over fuzzy domain

Xiangting Shi  1 , Ahmad Aziz Al Ahmadi  2 , Muhammad Bilal Khan  3 , Loredana Ciurdariu  4 , Khalil Hadi Hakami  5
Affiliations

Novel versions of Hölder's-Like and related inequalities with newly defined L P space, and their applications over fuzzy domain

Xiangting Shi et al. Heliyon. .

Abstract

It is widely recognized that fuzzy number theory relies on the characteristic function. However, within the fuzzy realm, the characteristic function transforms into a membership function contingent upon the interval [0,1]. This implies that real numbers and intervals represent exceptional cases of fuzzy numbers. By considering this approach, this paper introduces a new L P space and novel refinements for integral variations of Hölder's inequality which is known as Hölder's-like inequality over fuzzy domain. Numerous prevailing inequalities associated with Hölder's-like inequality can be enhanced through the newly acquired inequalities, as demonstrated through an application. By using newly defined special means, some new versions of integral inequalities have obtained where differentiable mappings are real-valued convex-like (or convex fuzzy) mappings Lastly, nontrivial numerical examples are also included to validate the accuracy of the presented inequalities as they vary with the parameter ꙍ .

Keywords: L P space over fuzzy domain; Beckenbach's-like inequality over fuzzy domain; Differentiable convex like mapping; Fuzzy special means; Fuzzy-number; Hölder-like inequality; Minkowski's-like inequality.

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Conflict of interest statement

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Loredana Ciurdariu reports article publishing charges was provided by Politehnica University Timisoara Department of Mathematics. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Fig. 1
Fig. 1
Triangular fuzzy number.
Fig. 2
Fig. 2
Trapezoidal fuzzy number.
See this image and copyright information in PMC

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