On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Nie, Dongming; Rashid, Saima; Akdemir, Ahmet Ocak; Băleanu, Dumitru; Liu, Jia‐Bao

doi:10.3390/math7080727

Cited by 31 publications

(16 citation statements)

References 19 publications

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“…The noteworthy scope of uses of the integral inequalities on convexity for both derivation and integration, while also maintaining the symmetry of sets and functions has been a subject of discourse for a long while. These variants had been progressed by means of various analysts [9][10][11][12][13]. Sarikaya et al [14] utilized the concepts of fractional calculus for deriving a bulk of variants that essentially depend on Hermite-Hadamard inequality.…”

Section: Introductionmentioning

confidence: 99%

New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

et al. 2020

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In Hilbert space, we develop a novel framework to study for two new classes of convex function depending on arbitrary non-negative function, which is called a predominating ℏ-convex function and predominating quasiconvex function, with respect to η , are presented. To ensure the symmetry of data segmentation and with the discussion of special cases, it is shown that these classes capture other classes of η -convex functions, η -quasiconvex functions, strongly ℏ-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of κ -fractional integral operator to generate novel variants related to the Hermite–Hadamard type for p t h -order differentiability. It is hoped that this research study will open new doors for in-depth investigation in convexity theory frameworks of a varying nature.

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Section: Introductionmentioning

confidence: 99%

New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

et al. 2020

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“…Fractional integral operators are very useful in mathematical inequalities. e authors have established fractional integral inequalities due to different fractional integral operators, see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Many authors have used Mittag-Leffler function to define fractional integral operators.…”

Section: Introductionmentioning

confidence: 99%

Boundedness of Fractional Integral Operators Containing Mittag-Leffler Function via Exponentially s-Convex Functions

Farid

Nazeer

et al. 2020

Journal of Mathematics

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The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

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“…For more details on inequalities, we refer the interested reader to [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

et al. 2019

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In this paper, we present a new definition of higher-order generalized strongly preinvex functions. Moreover, it is observed that the new class of higher-order generalized strongly preinvex functions characterize various new classes as special cases. We acquire a new q 1 q 2 -integral identity, then employing this identity, we establish several two-variable q 1 q 2 -integral inequalities of Simpson-type within a class of higher-order generalized strongly preinvex and quasi-preinvex functions. Finally, the utilities of our numerical approximations have concrete applications.

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On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Cited by 31 publications

References 19 publications

New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating ℏ-Convex Functions in Hilbert Space

Boundedness of Fractional Integral Operators Containing Mittag-Leffler Function via Exponentially s-Convex Functions

Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions

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