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New quantum variants of Simpson-Newton type inequalities via $(\alpha,m)$-convexity

Saad Ihsan Butt|Qurat Ul Ain|Huseyin Budak
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2023.06|한국수학논문집 (Korean Journal of Mathematics)|제31권 제2호|pp. 161-180

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키워드

Quantum calculus$(alphaSimpson's inequalityNewton's inequalitym)$-convexity
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초록

In this article, we will utilize $(\alpha, m)$-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using $q_{\varrho_{1}}$-integral and $q_{\varrho_{1}}$-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as H\"{o}lder's and Power mean, have been used to acquire new bounds.

Abstract

In this article, we will utilize $(\alpha, m)$-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using $q_{\varrho_{1}}$-integral and $q_{\varrho_{1}}$-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as H\"{o}lder's and Power mean, have been used to acquire new bounds.

참고문헌 (29)

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