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ON m-CONVEX SETS IN PRECONVEXITY SPACES
Min, Won-Keun The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
In this paper, we introduce the concepts of m-convex set, mcconvex function and $m^*c$-convex function. We study basic properties for m-convex sets and characterization for such functions.
On m-convex sets in preconvexity spaces
민원근 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
In this paper, we introduce the concepts of m-convex set, mc-convex function and m^*c-convex function. We study basic properties for m-convex sets and characterization for such functions.
Saima Rashid,Muhammad Aslam Noor,Khalida Inayat Noor 강원경기수학회 2019 한국수학논문집 Vol.27 No.4
In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.
Kang Shin Min,Farid Ghulam,Nazeer Waqas,Usman Muhammad 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
In this paper we have established a new identity for Katugampola fractional integrals. By using it we have found some generalizations of Riemann-Liouville fractional integral inequalities of Ostrowski type for (α,m)-convex functions. Also we prove some inequalities by taking particular appropriate values of α and m.
Ghulam Farid,Saira Bano Akbar,Laxmi Rathour,Lakshmi Narayan Mishra 강원경기수학회 2021 한국수학논문집 Vol.29 No.4
The refinement of an inequality provides better convergence of one quantity towards the other one. We have established the refinements of Hadamard inequalities for Riemann-Liouville fractional integrals via strongly $({\alpha},m)$-convex functions. In particular, we obtain two refinements of the classical Hadamard inequality. By using some known integral identities we also give refinements of error bounds of some fractional Hadamard inequalities.
On Generalizations of the Hadamard Inequality for (α, m)-Convex Functions
Set, Erhan,Sardari, Maryam,Ozdemir, Muhamet Emin,Rooin, Jamal Department of Mathematics 2012 Kyungpook mathematical journal Vol.52 No.3
In this paper we establish several Hadamard-type integral inequalities for (${\alpha}$, m)-convex functions.
Artion Kashuri,Rozana Liko,Muhammad Adil Khan,Arshad Iqbal 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.2
In this article, we first presented some integral inequalities for Gauss-Jacobi type quadrature formula involving generalized relative semi-(r; m, p, q, h1, h2)-preinvex mappings. And then, a new identity concerning twice differentiable mappings defined on m-invex set via conformable fractional integrals is derived. By using the notion of generalized relative semi- (r;m,p,q,h1,h2)-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via conformable fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.
GHULAM FARID,LAXMI RATHOUR,SIDRA BIBI,MUHAMMAD SAEED AKRAM,LAKSHMI NARAYAN MISHRA,VISHNU NARAYAN MISHRA The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.
Ghulam Farid,Laxmi Rathour,Muhammad Saeed Akram,Sidra Bibi,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined ($\alpha$,$h$-$m$)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function $h$ is bounded above by $\frac{1}{\sqrt{2}}$.
Ostrowski's Type Inequalities for (α, m)-Convex Function
Ozdemir, Muhamet Emin,Kavurmaci, Havva,Set, Erhan Department of Mathematics 2010 Kyungpook mathematical journal Vol.50 No.3
In this paper, we establish new inequalities of Ostrowski's type for functions whose derivatives in absolute value are (${\alpha}$, m)-convex.