Study of inequalities for unified integral operators of generalized convex functions

Published on Dec 31, 2021in Journal of Mass Spectrometry1.671
· DOI :10.30538/OMS2021.0147
Ghulam Farid16
Estimated H-index: 16
,
K. Mahreen1
Estimated H-index: 1
,
Yu-Ming Chu1
Estimated H-index: 1
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In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null null nu...
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Convexity theory becomes a hot area of research due to its applications in pure and applied mathematics, especially in optimization theory. The aim of this paper is to introduce a broader class of convex functions by unifying geometrically strong convex function with null null null null null null convex functions. This new class of functions is called as generalized geometrically strongly modified null null null null null null - convex functions. We established Hermite–Hadamard-type inequalities...
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#1Yan Zhao (Xinxiang Medical University)
#2M. Shoaib Saleem (University of Okara)
Last. Zabidin Salleh (UMT: Universiti Malaysia Terengganu)H-Index: 8
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Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of null null null null null null - exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomple...
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Last. Muhammad Imran (University of Okara)
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The theory of convex functions plays an important role in the study of optimization problems. The fractional calculus has been found the best to model physical and engineering processes. The aim of this paper is to study some properties of strongly convex functions via the Caputo–Fabrizio fractional integral operator. In this paper, we present Hermite–Hadamard-type inequalities for strongly convex functions via the Caputo–Fabrizio fractional integral operator. Some new inequalities of strongly c...
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Convexity plays an important role in many areas of mathematics, especially in the study of optimization problems where they are distinguished by a number of convenient properties. Our aim is to introduce a more extended version of convexity. In this paper, we introduced interval-valued generalized convex function and proved Hermite–Hadamard-, Jensen-, and Ostrowski-type inequalities in this generalization. The presented results are generalizations of many existing results of literature.
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Last. Chahn Yong Jung (CUI: COMSATS Institute of Information Technology)
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In this paper we study the Fejer-Hadamard inequalities for convex function with respect to a strictly monotone function. We establish two inequalities for convex function with respect to a strictly monotone function via Riemann-Liouville fractional integrals. From inequalities found here many new results can be derived by selecting specific strictly monotone and weight functions. Also a variety of existing Fejer-Hadamard and Hadamard inequalities can be reproduced.
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