Symmetric quantum calculus in interval valued frame work: operators and applications

Yuanheng Wang; Muhammad Zakria Javed; Muhammad Uzair Awan; Bandar Bin-Mohsin; Badreddine Meftah; Savin Treanta; Yuanheng Wang; Muhammad Zakria Javed; Muhammad Uzair Awan; Bandar Bin-Mohsin; Badreddine Meftah; Savin Treanta

doi:10.3934/math.20241343

AIMS Mathematics

2024, Volume 9, Issue 10: 27664-27686. doi: 10.3934/math.20241343

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Research article

Symmetric quantum calculus in interval valued frame work: operators and applications

1.
School of Mathematical Sciences Zhejiang Normal University, Jinhua 321004, China
2.
Department of Mathematics, Government College University, Faisalabad, Pakistan
3.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
4.
Laboratory of Analysis and Control of Differential Equations 'ACED', Department of Mathematics, University of 8 May 1945, Guelma 24000, Algeria
5.
Faculty of Applied Sciences, National University of Science and Technology Politehnica Bucharest, Bucharest 060042, Romania
6.
Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania
7.
Fundamental Sciences Applied in Engineering-Research Center, National University of Science and Technology Politehnica Bucharest, Bucharest 060042, Romania

Received: 02 August 2024 Revised: 05 September 2024 Accepted: 12 September 2024 Published: 24 September 2024
MSC : 26A33, 26A51, 26D07, 26D10, 26D15, 26D20

The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued $ (\mathcal{I}.\mathcal{V}) $ right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the $ (\mathcal{I}.\mathcal{V}) $ symmetric derivative operator, we develop the right-sided $ (\mathcal{I}.\mathcal{V}) $ integral operator and explore its key properties. Also, we establish various $ (\mathcal{I}.\mathcal{V}) $ trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results.
- interval-valued,
- Hukuhara difference,
- symmetric,
- quantum,
- convex,
- function,
- Hermite-Hadamard
Citation: Yuanheng Wang, Muhammad Zakria Javed, Muhammad Uzair Awan, Bandar Bin-Mohsin, Badreddine Meftah, Savin Treanta. Symmetric quantum calculus in interval valued frame work: operators and applications[J]. AIMS Mathematics, 2024, 9(10): 27664-27686. doi: 10.3934/math.20241343

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Abstract

The primary emphasis of the present study is to introduce some novel characterizations of the interval-valued $ (\mathcal{I}.\mathcal{V}) $ right symmetric quantum derivative and antiderivative operators relying on generalized Hukuhara difference. To continue the study, we start with the concept of symmetric differentiability in the interval-valued sense and explore some important properties. Furthermore, through the utilization of the $ (\mathcal{I}.\mathcal{V}) $ symmetric derivative operator, we develop the right-sided $ (\mathcal{I}.\mathcal{V}) $ integral operator and explore its key properties. Also, we establish various $ (\mathcal{I}.\mathcal{V}) $ trapezium-like inequalities by considering the newly proposed operators and support line. Later on, we deliver another proof of the trapezium inequality through an analytical approach. Also, we present the numerical and visual analysis for the verification of our results.

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