Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Waqar Afzal, Khurram Shabbir, Mubashar Arshad, Joshua Kiddy K. Asamoah, Ahmed M. Galal and Ching-Feng Wen

Journal of Mathematics, 2023, vol. 2023, 1-14

Abstract: In interval analysis, integral inequalities are determined based on different types of order relations, including pseudo, fuzzy, inclusion, and various other partial order relations. By developing a link between center-radius (CR) order relations, it seeks to develop a theory of inequalities with novel estimates. A (CR)-order relation relationship differs from traditional interval-order relationships in that it is calculated as follows: q=qc,qr=q¯+q¯/2,q¯−q¯/2. There are several advantages to using this ordered relationship, including the fact that the inequality terms deduced from it yield much more precise results than any other partial-order relation defined in the literature. This study introduces the concept of harmonical h1,h2-convex functions associated with the center-radius order relations, which is very novel in literature. Applied to uncertainty, the center-radius order relation is an effective tool for studying inequalities. Our first step was to establish the Hermite−Hadamard H.H inequality and then to establish Jensen inequality using these notions. We discuss a few exceptional cases that could have practical applications. Moreover, examples are provided to verify the applicability of the theory developed in the present study.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8865992

DOI: 10.1155/2023/8865992

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