Some well known inequalities on two dimensional convex mappings by means of Pseudo $ \mathcal{L-R} $ interval order relations via fractional integral operators having non-singular kernel

Zareen A. Khan; Waqar Afzal; Mujahid Abbas; Jong-Suk Ro; Abdullah A. Zaagan; Zareen A. Khan; Waqar Afzal; Mujahid Abbas; Jong-Suk Ro; Abdullah A. Zaagan

doi:10.3934/math.2024778

AIMS Mathematics

2024, Volume 9, Issue 6: 16061-16092. doi: 10.3934/math.2024778

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Research article

Some well known inequalities on two dimensional convex mappings by means of Pseudo $ \mathcal{L-R} $ interval order relations via fractional integral operators having non-singular kernel

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
3.
Department of Medical Research, China Medical University, Taichung 406040, Taiwan
4.
School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
5.
Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea
6.
Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia

Received: 01 March 2024 Revised: 10 April 2024 Accepted: 15 April 2024 Published: 07 May 2024
MSC : 26A48, 26A51, 33B10, 39A12, 39B62

Fractional calculus and convex inequalities combine to form a comprehensive mathematical framework for understanding and analyzing a variety of problems. This note develops Hermite-Hadamard, Fejér, and Pachpatte type integral inequalities within pseudo left-right order relations by applying fractional operators with non-singular kernels. Recently, results have been developed using classical Riemann integral operators in addition to various other partial order relations that have some defects that we explained in literature in order to demonstrate the unique characteristics of pseudo order relations. To verify the developed results, we constructed several interesting examples and provided a number of remarks that demonstrate that this type of fractional operator generalizes several previously published results when different things are set up. This work can lead to improvements in mathematical theory, computational methods, and applications across a wide range of disciplines.
- Hermite-Hadamard,
- Fejér,
- Pachpatte type inequality,
- pseudo order,
- interval-valued
Citation: Zareen A. Khan, Waqar Afzal, Mujahid Abbas, Jong-Suk Ro, Abdullah A. Zaagan. Some well known inequalities on two dimensional convex mappings by means of Pseudo $ \mathcal{L-R} $ interval order relations via fractional integral operators having non-singular kernel[J]. AIMS Mathematics, 2024, 9(6): 16061-16092. doi: 10.3934/math.2024778

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Abstract

Fractional calculus and convex inequalities combine to form a comprehensive mathematical framework for understanding and analyzing a variety of problems. This note develops Hermite-Hadamard, Fejér, and Pachpatte type integral inequalities within pseudo left-right order relations by applying fractional operators with non-singular kernels. Recently, results have been developed using classical Riemann integral operators in addition to various other partial order relations that have some defects that we explained in literature in order to demonstrate the unique characteristics of pseudo order relations. To verify the developed results, we constructed several interesting examples and provided a number of remarks that demonstrate that this type of fractional operator generalizes several previously published results when different things are set up. This work can lead to improvements in mathematical theory, computational methods, and applications across a wide range of disciplines.

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