Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Kalsoom, HumairaPublisher: search.filters.publisher.Mdpi

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 85
    Citation - Scopus: 108
    Inequalities by Means of Generalized Proportional Fractional Integral Operators With Respect To Another Function
    (Mdpi, 2019) Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; Rashid, Saima
    In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Psi. The authors prove several inequalities for newly defined GPF-integral with respect to another function Psi. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Psi and the proportionality index sigma. Furthermore, we present the application of the novel operator with several integral inequalities. A few new properties are exhibited, and the numerical approximation of these new operators is introduced with certain utilities to real-world problems.
  • Article
    Citation - WoS: 24
    Citation - Scopus: 23
    Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions
    (Mdpi, 2020) Rashid, Saima; Idrees, Muhammad; Chu, Yu -Ming; Baleanu, Dumitru; Kalsoom, Humaira
    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 q1q2-integral identity, then employing this identity, we establish several two-variable q1q2-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.
  • 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: 24
    Citation - Scopus: 20
    Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function Correlated With Coordinated Generalized Φ-Convex Functions
    (Mdpi, 2020) Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Chu, Yu-Ming; Baleanu, Dumitru; Chu, Hong-Hu
    In this paper, the newly proposed concept of Raina's function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag-Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q1q2-differentiable function by inserting Raina's functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized phi-convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina's function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.
  • Article
    Citation - WoS: 36
    Citation - Scopus: 33
    Post Quantum Integral Inequalities of Hermite-Hadamard Associated With Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre Mappings
    (Mdpi, 2020) Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Akram, Saima; Baleanu, Dumitru; Chu, Yu-Ming; Kalsoom, Humaira
    By using the contemporary theory of inequalities, this study is devoted to proposing a number of refinements inequalities for the Hermite-Hadamard's type inequality and conclude explicit bounds for two new definitions of (p(1)p(2), q(1)q(2))-differentiable function and (p(1)p(2), q(1)q(2))-integral for two variables mappings over finite rectangles by using pre-invex set. We have derived a new auxiliary result for (p(1)p(2), q(1)q(2))-integral. Meanwhile, by using the symmetry of an auxiliary result, it is shown that novel variants of the the Hermite-Hadamard type for (p(1)p(2), q(1)q(2))-differentiable utilizing new definitions of generalized higher-order strongly pre-invex and quasi-pre-invex mappings. It is to be acknowledged that this research study would develop new possibilities in pre-invex theory, quantum mechanics and special relativity frameworks of varying nature for thorough investigation.