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Keywords = Hölder–İşcan integral inequality

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21 pages, 339 KB  
Article
New Integral Inequalities via Generalized Preinvex Functions
by Muhammad Tariq, Asif Ali Shaikh, Soubhagya Kumar Sahoo, Hijaz Ahmad, Thanin Sitthiwirattham and Jiraporn Reunsumrit
Axioms 2021, 10(4), 296; https://doi.org/10.3390/axioms10040296 - 7 Nov 2021
Cited by 11 | Viewed by 2015
Abstract
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 [...] Read more.
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 Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan 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. Full article
18 pages, 342 KB  
Article
Hermite–Hadamard Type Inequalities Involving k-Fractional Operator for (h¯,m)-Convex Functions
by Soubhagya Kumar Sahoo, Hijaz Ahmad, Muhammad Tariq, Bibhakar Kodamasingh, Hassen Aydi and Manuel De la Sen
Symmetry 2021, 13(9), 1686; https://doi.org/10.3390/sym13091686 - 13 Sep 2021
Cited by 45 | Viewed by 3224
Abstract
The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel [...] Read more.
The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented. Full article
11 pages, 276 KB  
Article
Better Approaches for n-Times Differentiable Convex Functions
by Praveen Agarwal, Mahir Kadakal, İmdat İşcan and Yu-Ming Chu
Mathematics 2020, 8(6), 950; https://doi.org/10.3390/math8060950 - 10 Jun 2020
Cited by 31 | Viewed by 2478
Abstract
In this work, by using an integral identity together with the Hölder–İşcan inequality we establish several new inequalities for n-times differentiable convex and concave mappings. Furthermore, various applications for some special means as arithmetic, geometric, and logarithmic are given. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
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