Browsing by Author "Kalsoom, Humaira"

Now showing 1 - 13 of 13

Citation Count: Rashid, Saima...et al. (2019). "Inequalities by means of generalized proportional fractional integral operators with respect to another function", Mathematics, Vol. 7, No. 12.
Inequalities by means of generalized proportional fractional integral operators with respect to another function
(2019) Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; Chu, Yu-Ming; 234808
In this article, we define a new fractional technique which is known as generalized proportional fractional (GPF) integral in the sense of another function Ψ. The authors prove several inequalities for newly defined GPF-integral with respect to another function Ψ. Our consequences will give noted outcomes for a suitable variation to the GPF-integral in the sense of another function Y and the proportionality index ζ. 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. © 2019 by the authors.
Citation Count: Chu, Yu-Ming...et al. (2021). "More new results on integral inequalities for generalized K-fractional conformable integral operators", Discrete and Continuous Dynamical Systems - Series S, Vol. 14, No. 7, pp. 2119-2135.
More new results on integral inequalities for generalized K-fractional conformable integral operators
(2021) Chu, Yu-Ming; Rashid, Saima; Jarad, Fahd; Noor, Muhammad Aslam; Kalsoom, Humaira; 234808
This paper aims to investigate the several generalizations by newly proposed generalized K-fractional conformable integral operator. Based on these novel ideas, we derived a novel framework to study for Ceby sev and Pólya-Szegö type inequalities by generalized K-fractional conformable integral operator. Several special cases are apprehended in the light of generalized fractional conformable integral. This novel strategy captures several existing results in the relative literature. We also aim at showing important connections of the results here with those including Riemann-Liouville fractional integral operator. © 2021 American Institute of Mathematical Sciences. All rights reserved.
Citation Count: Kalsoom, Humaira...et al. (2020). "New (p, q)-estimates for different types of integral inequalities via (alpha, m)-convex mappings", Open Physics, Vol. 18, pp. 1830-1854.
New (p, q)-estimates for different types of integral inequalities via (alpha, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.p>
Citation Count: Kalsoom, Humaira;...et.al. (2020). "New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings", Open Mathematics, Vol.18, No.1, pp.1830-1854.
New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings
(2020) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (α, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.
Citation Count: Kalsoom, Humaira..et al. (2021). "New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings", OPEN MATHEMATICS, Vol. 18, pp. 1830-1854.
New (p, q)-estimates for different types of integral inequalities via (α, m)-convex mappings
(2021) Kalsoom, Humaira; Latif, Muhammad Amer; Rashid, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In the article, we present a new (p, q)-integral identity for the first-order (p, q)-differentiable functions and establish several new (p, q)-quantum error estimations for various integral inequalities via (a alpha, m)-convexity. We also compare our results with the previously known results and provide two examples to show the superiority of our obtained results.
Citation Count: Zhou, Shuang-Shuang...et al. (2020). "New estimates considering the generalized proportional Hadamard fractional integral operators", Advances in Difference Equations, Vol. 2020, No. 1.
New estimates considering the generalized proportional Hadamard fractional integral operators
(2020) Zhou, Shuang-Shuang; Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; 234808
In the article, we describe the Grüss type inequality, provide some related inequalities by use of suitable fractional integral operators, address several variants by utilizing the generalized proportional Hadamard fractional (GPHF) integral operator. It is pointed out that our introduced new integral operators with nonlocal kernel have diversified applications. Our obtained results show the computed outcomes for an exceptional choice to the GPHF integral operator with parameter and the proportionality index. Additionally, we illustrate two examples that can numerically approximate these operators. © 2020, The Author(s).
Citation Count: Kalsoom, Humaira...et al. (2020). "New Estimates of q(1)q(2)-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions", Journal of Function Spaces, Vol. 2020.
New Estimates of q(1)q(2)-Ostrowski-Type Inequalities within a Class of n-Polynomial Prevexity of Functions
(2020) Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is calledn-polynomial preinvex functions. We use then-polynomial preinvex functions to develop q(1)q(2)-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q(1)q(2)-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q(1)q(2)-analogues of the Ostrowski-type integrals inequalities which are connected with then-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.
Citation Count: Kalsoom, Humaira;...et.al. (2020). "New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions", Journal of Function Spaces, Vol.2020.
New Estimates of q1q2 -Ostrowski-Type Inequalities within a Class of n -Polynomial Prevexity of Functions
(2020) Kalsoom, Humaira; Idrees, Muhammad; Baleanu, Dumitru; Chu, Yu-Ming; 56389
In this article, we develop a novel framework to study for a new class of preinvex functions depending on arbitrary nonnegative function, which is called n-polynomial preinvex functions. We use the n-polynomial preinvex functions to develop q1q2-analogues of the Ostrowski-type integral inequalities on coordinates. Different features and properties of excitement for quantum calculus have been examined through a systematic way. We are discussing about the suggestions and different results of the quantum inequalities of the Ostrowski-type by inferring a new identity for q1q2-differentiable function. However, the problem has been proven to utilize the obtained identity, we give q1q2-analogues of the Ostrowski-type integrals inequalities which are connected with the n-polynomial preinvex functions on coordinates. Our results are the generalizations of the results in earlier papers.
Citation Count: Rashid, Saima...et al. (2020). "New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space", Symmetry-Basel, Vol. 12, No. 2.
New Multi-Parametrized Estimates Having pth-Order Differentiability in Fractional Calculus for Predominating h-Convex Functions in Hilbert Space
(2020) Rashid, Saima; Kalsoom, Humaira; Hammouch, Zakia; Ashraf, Rehana; Baleanu, Dumitru; Chu, Yu-Ming; 56389
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.
Citation Count: Rashid, Saima...et al. (2020). "On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals", Advances in Difference Equations, Vol. 2020, No. 1.
On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals
(2020) Rashid, Saima; Jarad, Fahd; Kalsoom, Humaira; Chu, Yu-Ming; 234808
In this paper, we introduce the generalized k-fractional integral in terms of a new parameter k> 0 , present some new important inequalities of Pólya–Szegö and Čebyšev types by use of the generalized k-fractional integral. Our consequences with this new integral operator have the abilities to implement the evaluation of many mathematical problems related to real world applications.
Citation Count: Kalsoom, Humaira...et al. (2020). "Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings", Symmetry-Basel, Vol. 12, No. 3.
Post Quantum Integral Inequalities of Hermite-Hadamard-Type Associated with Co-Ordinated Higher-Order Generalized Strongly Pre-Invex and Quasi-Pre-Invex Mappings
(2020) Kalsoom, Humaira; Rashid, Saima; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Akram, Saima; Baleanu, Dumitru; Chu, Yu-Ming; 56389
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.
Citation Count: Chu, Hong-Hu...et al. (2020). "Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function correlated with Coordinated Generalized phi-Convex Functions", Symmetry-Basel, Vol. 12, No. 2.
Quantum Analogs of Ostrowski-Type Inequalities for Raina's Function correlated with Coordinated Generalized phi-Convex Functions
(2020) Chu, Hong-Hu; Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Safdar, Farhat; Chu, Yu-Min; Baleanu, Dumitru; 56389
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.
Citation Count: Kalsoom, Humaira...et al. (2020). "Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions", Symmetry-Basel, Vol. 12, No. 1.
Two-Variable Quantum Integral Inequalities of Simpson-Type Based on Higher-Order Generalized Strongly Preinvex and Quasi-Preinvex Functions
(2020) Kalsoom, Humaira; Rashid, Saima; Idrees, Muhammad; Chu, Yu -Ming; Baleanu, Dumitru; 56389
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.