Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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20203

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Author: search.filters.author.Chu, Yu-MingSubject: search.filters.subject.Convex Function

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 22
    Citation - Scopus: 24
    Some New Extensions for Fractional Integral Operator Having Exponential in the Kernel and Their Applications in Physical Systems
    (de Gruyter Poland Sp Z O O, 2020) Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima
    The key purpose of this study is to suggest a new fractional extension of Hermite-Hadamard, Hermite-Hadamard-Fejer and Pachpatte-type inequalities for harmonically convex functions with exponential in the kernel. Taking into account the new operator, we derived some generalizations that capture novel results under investigation with the aid of the fractional operators. We presented, in general, two different techniques that can be used to solve some new generalizations of increasing functions with the assumption of convexity by employing more general fractional integral operators having exponential in the kernel have yielded intriguing results. The results achieved by the use of the suggested scheme unfold that the used computational outcomes are very accurate, flexible, effective and simple to perform to examine the future research in circuit theory and complex waveforms.
  • Article
    Citation - WoS: 32
    Citation - Scopus: 51
    New Multi-Parametrized Estimates Having Pth-Order Differentiability in Fractional Calculus for Predominating H-Convex Functions in Hilbert Space
    (Mdpi, 2020) Kalsoom, Humaira; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima
    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 PLANCK CONSTANT OVER TWO PI-convex function and predominating quasiconvex function, with respect to eta, 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 eta-convex functions, eta-quasiconvex functions, strongly PLANCK CONSTANT OVER TWO PI-convex functions of higher-order and strongly quasiconvex functions of a higher order, etc. Meanwhile, an auxiliary result is proved in the sense of kappa-fractional integral operator to generate novel variants related to the Hermite-Hadamard type for pth-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.
  • Article
    Citation - WoS: 69
    Citation - Scopus: 90
    Generation of New Fractional Inequalities Via N Polynomials S-Type Convexity With Applications
    (Springer, 2020) Iscan, Imdat; Baleanu, Dumitru; Chu, Yu-Ming; Rashid, Saima
    The celebrated Hermite-Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite-Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivatives in absolute value at certain powers are n-polynomial s-type convex functions by employing K-fractional integral operators have yielded intriguing results. Applications and motivations of presented results are briefly discussed that generate novel variants related to quadrature rules that will be helpful for in-depth investigation in fractal theory, optimization and machine learning.