Browsing by Author "Ifra Bashir Sial"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
Item A new variant of Jensen inclusion and Hermite-Hadamard type inclusions for interval-valued functions(University of Nis, 2023) Thanin Sitthiwirattham; Ifra Bashir Sial; Muhammad Aamir Ali; HŸseyin Budak; Jiraporn Reunsumrit; M.A. Ali; Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.comIn this research, we give a new version of Jensen inclusion for interval-valued functions, which is called Jensen-Mercer inclusion. Moreover, we establish some new inclusions of the Hermite-Hadamard-Mercer type for interval-valued functions. Finally, we give some applications of newly established inequalities to make them more interesting for the readers. © 2023, University of Nis. All rights reserved.Item On some new inequalities of hermiteÐhadamard midpoint and trapezoid type for preinvex functions in (P, q)-calculus(MDPI, 2021) Ifra Bashir Sial; Muhammad Aamir Ali; Ghulam Murtaza; Sotiris K. Ntouyas; Jarunee Soontharanon; 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; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we establish some new HermiteÐHadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for (p, q)-differentiable preinvex functions in the context of (p, q)-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item On Some New OstrowskiÐMercer-Type Inequalities for Differentiable Functions(MDPI, 2022) Ifra Bashir Sial; Nichaphat Patanarapeelert; Muhammad Aamir Ali; HŸseyin Budak; 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; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.thIn this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some OstrowskiÐMercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.Item On some new simpsonÕs formula type inequalities for convex functions in post-quantum calculus(MDPI, 2021) Miguel J. Vivas-Cortez; Muhammad Aamir Ali; Shahid Qaisar; Ifra Bashir Sial; Sinchai Jansem; Abdul Mateen; M.J. Vivas-Cortez; Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat—lica del Ecuador, Escuela de Ciencias Matem‡ticas y F’sicas, Quito, Av. 12 de Octubre 1076, Apartado, 17-01-2184, Ecuador; email: mjvivas@puce.edu.ec; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.comIn this work, we prove a new (p, q)-integral identity involving a (p, q)-derivative and (p, q)-integral. The newly established identity is then used to show some new SimpsonÕs formula type inequalities for (p, q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Item Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions(MDPI, 2022) Thanin Sitthiwirattham; Ghulam Murtaza; Muhammad Aamir Ali; Chanon Promsakon; Ifra Bashir Sial; Praveen Agarwal; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.comIn this study, first we establish a (p, q)-integral identity involving the second (p, q)-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-(p, q)-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.