Novel q-Differentiable Inequalities

Author:

Zuo Xuewu1ORCID,Butt Saad Ihsan2ORCID,Umar Muhammad2ORCID,Budak Hüseyin3ORCID,Ali Muhammad Aamir4ORCID

Affiliation:

1. General Education Department, Anhui Xinhua University, Hefei 230088, China

2. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan

3. Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Türkiye

4. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

Abstract

The striking goal of this study is to introduce a q-identity for a parameterized integral operator via differentiable function. First, we discover the parameterized lemma for the q-integral. After that, we provide several q-differentiable inequalities. By taking suitable choices, some interesting results are obtained. With all of these, we displayed the findings from the traditional analysis utilizing q→1−.

Funder

Natural Science Foundation of Anhui Province Higher School

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference30 articles.

1. Mitrinović, D.S., Pečarić, J.E., and Fink, A.M. (1993). Classical and New Inequalities in Analysis, Mathematics and Its Applications, Kluwer Academic Publishers Group.

2. Dragomir, S.S., and Pearce, C.E.M. (2000). Selected Topics on Hermite-Hadamard Inequalities and Applications, Victoria University. RGMIA Monographs.

3. Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula;Kirmaci;Appl. Math. Comput.,2004

4. Some Hermite–Hadamard type inequalities for differentiable convex functions and applications;Qi;Hacet. J. Math. Stat.,2013

5. Butt, S.I., and Pečarić, J. (2018). Popoviciu’S Inequality for n-Convex Functions, Lap Lambert Academic Publishing.

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