Quantum symmetric analysis of interval-valued mappings based on generalized Hukuhara differences

Volume 40, Issue 1, pp 1--21 https://dx.doi.org/10.22436/jmcs.040.01.01

Publication Date: May 29, 2025 Submission Date: December 03, 2024 Revision Date: February 12, 2025 Accteptance Date: March 11, 2025

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Authors

M. Z. Javed - Department of Mathematics, Government College University, Faisalabad, Pakistan. M. U. Awan - Department of Mathematics, Government College University, Faisalabad, Pakistan. C.-E. Stoenoiu - Department of Electric Machines and Drives, Technical University of Cluj-Napoca, Cluj-Napoca 400027, Romania. D.-A. Iluțiu-Varvara - Faculty of Building Services Engineering, Technical University of Cluj-Napoca, Cluj-Napoca 400114, Romania. L. Jäntschi - Department of Physics and Chemistry, Technical University of Cluj-Napoca, Cluj-Napoca 400641, Romania. S. S. Dragomir - Department of Mathematics, College of Engineering \(\&\) Science, Victoria University, Melbourne City, MC 8001, Australia.

Abstract

The primary aim of this investigation is to examine the quantum symmetric differentiability and anti-derivative characteristics of interval-valued (I.V.) mappings utilizing generalized Hukuhara differences. Initially, we present the concepts of the I.V. left quantum symmetric derivative operator and offer its characterization. We present the left quantum symmetric integral operator and its essential properties, grounded in the newly proposed derivative operator. Subsequently, we examine their various essential properties. Finally, we present the applications of our proposed operators to integral inequalities concerning I.V. convex mappings and totally ordered convex mappings. Moreover, the validity of our results is corroborated by numerical and graphical representations.

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Keywords

• Convex mapping
• interval-valued mapping
• Hukuhara difference
• symmetric quantum
• center-radius
• Hermite-Hadamard inequality

MSC

•  26A51
•  26D07
•  26D10
•  26D15
•  26D20

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