Hyers-Ulam Stability of 2D-Convex Mappings and Some Related New Hermite-Hadamard, Pachpatte, and Fejér Type Integral Inequalities Using Novel Fractional Integral Operators via Totally Interval-Order Relations with Open Problem

被引：2

作者：

Afzal, Waqar ^{[1
,2
]}

Breaz, Daniel ^{[3
]}

Abbas, Mujahid ^{[2
,4
,5
]}

Cotirla, Luminita-Ioana ^{[6
]}

Khan, Zareen A. ^{[7
]}

Rapeanu, Eleonora ^{[8
]}

机构：

[1] Univ Gujrat, Dept Math, Gujrat 50700, Pakistan

[2] Govt Coll Univ, Dept Math, Katchery Rd, Lahore 54000, Pakistan

[3] 1 Decembrie 1918 Univ Alba Iulia, Dept Math, Alba Iulia 510009, Romania

[4] China Med Univ, Dept Med Res, Taichung, Taiwan

[5] Univ Pretoria, Dept Math & Appl Math, Lynnwood Rd, ZA-0002 Pretoria, South Africa

[6] Tech Univ Cluj Napoca, Dept Math, Cluj Napoca 400114, Romania

[7] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

[8] Mircea Cel Batran Naval Acad, Dept Math, Constanta 900218, Romania

来源：

MATHEMATICS | 2024年 / 12卷 / 08期

关键词：

Pachpatte's inequality; Hermite-Hadamard; Fejer inequality; 2D-convex functions; total order relation; Hyers-Ulam stability; fractional operators; CONVEX-FUNCTIONS; RECTANGLE;

D O I：

10.3390/math12081238

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to introduce a new type of two-dimensional convexity by using total-order relations. In the first part of this paper, we examine the Hyers-Ulam stability of two-dimensional convex mappings by using the sandwich theorem. Our next step involves the development of Hermite-Hadamard inequality, including its weighted and product forms, by using a novel type of fractional operator having non-singular kernels. Moreover, we develop several nontrivial examples and remarks to demonstrate the validity of our main results. Finally, we examine approximate convex mappings and have left an open problem regarding the best optimal constants for two-dimensional approximate convexity.

引用

页数：33