Browsing by Author "Mujahid Abbas"

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    Montgomery identity and Ostrowski-type inequalities via quantum calculus
    (De Gruyter Open Ltd, 2021) Thanin Sitthiwirattham; Muhammad Aamir Ali; Huseyin Budak; Mujahid Abbas; Saowaluck Chasreechai; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com
    In this paper, we prove a quantum version of Montgomery identity and prove some new Ostrowski-type inequalities for convex functions in the setting of quantum calculus. Moreover, we discuss several special cases of newly established inequalities and obtain different new and existing inequalities in the field of integral inequalities. © 2021 Thanin Sitthiwirattham et al., published by De Gruyter.
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    On generalizations of quantum SimpsonÕs and quantum newtonÕs inequalities with some parameters
    (American Institute of Mathematical Sciences, 2021) Chanon Promsakon; Muhammad Aamir Ali; HŸseyin Budak; Mujahid Abbas; Faheem Muhammad; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Department of Medical research, China Medical University Hospital, China, Medical University, Taichung, Taiwan; email: sit@dusit.ac.th
    In this paper, we prove two identities concerning quantum derivatives, quantum integrals, and some parameters. Using the newly proved identities, we prove new SimpsonÕs and NewtonÕs type inequalities for quantum differentiable convex functions with two and three parameters, respectively. We also look at the special cases of our key findings and find some new and old SimpsonÕs type inequalities, NewtonÕs type inequalities, midpoint type inequalities, and trapezoidal type inequalities. © 2021 the Author(s), licensee AIMS Press.