New quantum variants of Simpson-Newton type inequalities via $(\alpha,m)$-convexity
New quantum variants of Simpson-Newton type inequalities via $(\alpha,m)$-convexity
Saad Ihsan Butt(Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000 Pakistan); Qurat Ul Ain(COMSATS University Islamabad, Attock Campus, Pakistan.); Huseyin Budak(Department of Mathematics, Faculty of Science and Arts Du ̈zce University, Konuralp Campus, Du ̈zce,)
31권 2호, 161~180쪽
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.
- 발행기관:
- 강원경기수학회
- 분류:
- 수학