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ON APPROXIMATION PROPERTIES OF STANCU VARIANT λ-SZÁSZ-MIRAKJAN-DURRMEYER OPERATORS
Aslan, Resat,Rathour, Laxmi The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.3
In the present paper, we aim to obtain several approximation properties of Stancu form Szász-Mirakjan-Durrmeyer operators based on Bézier basis functions with shape parameter λ ∈ [-1, 1]. We estimate some auxiliary results such as moments and central moments. Then, we obtain the order of convergence in terms of the Lipschitz-type class functions and Peetre's K-functional. Further, we prove weighted approximation theorem and also Voronovskaya-type asymptotic theorem. Finally, to see the accuracy and effectiveness of discussed operators, we present comparison of the convergence of constructed operators to certain functions with some graphical illustrations under certain parameters.
A note on transversal hypersurfaces of para-Kenmotsu manifolds
Rajendra Prasad,Laxmi Rathour,Pooja Gupta,Abdul Haseeb 장전수학회 2023 Proceedings of the Jangjeon mathematical society Vol.26 No.1
A note on transversal hypersurfaces of para-Kenmotsu manifolds
GHULAM FARID,LAXMI RATHOUR,SIDRA BIBI,MUHAMMAD SAEED AKRAM,LAKSHMI NARAYAN MISHRA,VISHNU NARAYAN MISHRA The Korean Society for Computational and Applied M 2023 Journal of applied and pure mathematics Vol.5 No.1/2
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.
XHEVAT ZAHIR KRASNIQI,L. Rathour,Lakshmi Narayan Mishra 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.3
In this paper we have introduced the deferred generalized de la Vallée Poussin means. Using such means of partial sums of the Fourier series of continuous and periodic functions, we have proved some theorems pertaining to upper bound of such means, to the upper bound of the their deviation from the considered functions, and to the degree of approximation when such functions belong to Lipschitz classes.
Ghulam Farid,Laxmi Rathour,Muhammad Saeed Akram,Sidra Bibi,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 한국전산응용수학회 2023 Journal of Applied and Pure Mathematics Vol.5 No.1
The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined ($\alpha$,$h$-$m$)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function $h$ is bounded above by $\frac{1}{\sqrt{2}}$.
J. K. Kushwaha,Laxmi Rathour,Vishnu Narayan Mishra,Krishna Kumar 원광대학교 기초자연과학연구소 2022 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.24 No.3
A number of researchers (See [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) have determined the degree of approximation of functions belonging to Lipschitz classes, using Cesaro, Euler and generalized Nörlund and various product summability means. Recently Krasniqi [15] has determined the degree of approximation of conjugate of functions using (E,q)(C, α, β) means. Mishra and Khatri [7] also determined the degree of approximation by using (Np.E1) product means in the Hölder metric. In this paper, we have determined the degree of approximation of functions belonging to Lipschitz class and weighted class by using (N, p)(C, θ, β) means of Fourier series and conjugate series of Fourier series which in particular becomes (E, q)(C, θ, β).
Jitendra Kumar Kushwaha,Laxmi Rathour,Lakshmi Narayan Mishra,Krishna Kumar 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
In this paper, we have determined the degree of approximation of function belonging of Lipschitz class by using Deferred-Generalized N\"{o}rlund $ (D_\beta^\gamma.N_{pq})$ means of Fourier series and conjugate series of Fourier series, where $\{p_n\}$ and $\{q_n\}$ is a non-increasing sequence. So that results of DE\~{G}ER and BAYINDIR \cite{DEBA} become special cases of our results.
Effectiveness of various nonpharmacological analgesic methods in newborns
Kumar, Pancham,Sharma, Rakesh,Rathour, Sukhdev,Karol, Sunidhi,Karol, Mohit The Korean Pediatric Society 2020 Clinical and Experimental Pediatrics (CEP) Vol.63 No.1
Background: Pain during the developmental period may adversely affect developing neuronal pathways and result in adverse neurodevelopmental, cognitive, and behavioral effects in later life. Immunizations, e.g., hepatitis B vaccine (HBV), administered at birth are painful experiences to which neonates are universally subjected. Purpose: Here we aimed to study and compare the effectiveness of various nonpharmacological pain management methods in newborns to enable the development of safe and effective analgesic methods for newborns. Methods: This prospective study was conducted at a tertiary care hospital in the Himalayan region. Three hundred term healthy neonates were divided into 6 groups of 50 each. Groups 1-5 were intervention groups, patients of which received a nonpharmacological intervention (breastfeeding, nonnutritive sucking, rocking, 25% sucrose, or distilled water) before the intramuscular HBV, while patients in group 6 received no intervention. The pain response in each group after the HBV injection was assessed and compared using cry duration and Douleur Aigue Nveau-ne (DAN) score, a behavioral acute pain rating scale for newborns. Results: Cry duration was decreased in all intervention groups, significantly so in the sucrose (19.90 seconds), breastfeeding (31.57 seconds), and nonnutritive sucking (36.93 seconds) groups compared with controls (52.86 seconds). DAN scores decreased significantly (P<0.05) at one or more points i.e. 30, 60, or 120 seconds in the breastfeeding and 25% sucrose intervention groups compared with controls. Conclusion: Oral sucrose and nonnutritive sucking are simple yet underutilized nonpharmacological interventions that effectively reduce pain in newborns.