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

Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Chu, Yu‐Ming; Băleanu, Dumitru

doi:10.3390/sym12010051

Cited by 24 publications

(14 citation statements)

References 40 publications

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“…The continuous growth of interest has occurred in order to meet the requirements in needs of fertile applications of these inequalities. Such inequalities had been studied by many researchers who in turn used various techniques for the sake of exploring and offering these inequalities [31][32][33][34][35][36][37][38][39][40][41][42] and the references cited therein.…”

Section: Fuzzy Structures Functions Limitations On Functionsmentioning

confidence: 99%

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

et al. 2020

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T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.

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Section: Fuzzy Structures Functions Limitations On Functionsmentioning

confidence: 99%

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

et al. 2020

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“…Recently, Rashid et al [23] proposed the concepts of differentiable higher-order stronglyh-convex functions. Kalsoom et al [24] explored the higher-order strongly generalized preinvex function in a different way and presented several generalizations for two-variable quantum Simpson's-type inequalities. For more features and utilities of the strongly convex functions, see [25][26][27][28][29][30][31][32].…”

Section: Related Workmentioning

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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“…Recently, Lou et al [8] presented basic properties of Iq-calculus and derived Iq-Hermite-Hadamard inequalities for convex intervalvalued functions. For more details, see [9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

New Post Quantum Analogues of Hermite–Hadamard Type Inequalities for Interval-Valued Convex Functions

Kalsoom

Ali

Idrees³

et al. 2021

Mathematical Problems in Engineering

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The main objective of this paper is to introduce I p , q ϱ -derivative and I p , q ϱ -integral for interval-valued functions and discuss their key properties. Also, we prove the I p , q ϱ -Hermite–Hadamard inequalities for interval-valued functions is the development of p , q ϱ -Hermite–Hadamard inequalities by using new defined I p , q ϱ -integral. Moreover, we prove some results for midpoint- and trapezoidal-type inequalities by using the concept of Pompeiu–Hausdorff distance between the intervals. It is also shown that the results presented in this paper are extensions of some of the results already shown in earlier works. The proposed studies produce variants that would be useful for performing in-depth investigations on fractal theory, optimization, and research problems in different applied fields, such as computer science, quantum mechanics, and quantum physics.

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

Cited by 24 publications

References 40 publications

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

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

New Post Quantum Analogues of Hermite–Hadamard Type Inequalities for Interval-Valued Convex Functions

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