Browsing by Author "Soubhagya Kumar Sahoo"

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    A comprehensive analysis of hermiteÐhadamard type inequalities via generalized preinvex functions
    (MDPI, 2021) Muhammad Tariq; Hijaz Ahmad; HŸseyin Budak; Soubhagya Kumar Sahoo; Thanin Sitthiwirattham; Jiraporn Reunsumrit; T. Sitthiwirattham; Department of Mathematics, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known HermiteÐHadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
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    New integral inequalities via generalized preinvex functions
    (MDPI, 2021) Muhammad Tariq; Asif Ali Shaikh; Soubhagya Kumar Sahoo; Hijaz Ahmad; Thanin Sitthiwirattham; Jiraporn Reunsumrit; T. Sitthiwirattham; Department of Mathematics, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m-preinvex function and to present inequalities of the Hermite-Hadamard type in the setting of the generalized s-type m-preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite-Hadamard-type inequality using HšlderÕs integral inequality, the improved power-mean integral inequality, and the Hšlder-__can integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory. © 2021 by the authors.
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    Several integral inequalities of hermiteÐhadamard type related to k-fractional conformable integral operators
    (MDPI, 2021) Muhammad Tariq; Soubhagya Kumar Sahoo; Hijaz Ahmad; Thanin Sitthiwirattham; Jarunee Soontharanon; H. Ahmad; Section of Mathematics, International Telematic University Uninettuno, Roma, Corso Vittorio Emanuele II 39, 00186, Italy; email: f17ppbsi011@uetpeshawar.edu.pk; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we present some ideas and concepts related to the k-fractional conformable integral operator for convex functions. First, we present a new integral identity correlated with the k-fractional conformable operator for the first-order derivative of a given function. Employing this new identity, the authors have proved some generalized inequalities of HermiteÐHadamard type via HšlderÕs inequality and the power mean inequality. Inequalities have a strong correlation with convex and symmetric convex functions. There exist expansive properties and strong correlations between the symmetric function and various areas of convexity, including convex functions, probability theory, and convex geometry on convex sets because of their fascinating properties in the mathematical sciences. The results of this paper show that the methodology can be directly applied and is computationally easy to use and exact. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.