Browsing by Author "Idrees, Muhammad"

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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: 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.