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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,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 $\frac{1}{\sqrt{2}}$.
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 ${\frac{1}{\sqrt{2}}}$.
Radau quadrature for a rational almost quasi-Hermite-Fej{\'e}r-type interpolation
Shrawan Kumar,Neha Mathur,Laxmi Rathour,Vishnu Narayan Mishra,Pankaj Mathur 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
The aim of this paper is to obtain a Radau type quadrature formula for a rational interpolation process satisfying the almost quasi Hermite Fej\'er interpolatory conditions on the zeros of Chebyshev Markov sine fraction on $[-1, 1)$.
Lucas Veronez Goulart Ferreira,Laxmi Rathour,Devika Dabke,Fabio Roberto Chavarette,Vishnu Narayan Mishra 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.6
Rotating machines heavily rely on an intricate network of interconnected sub-components, with bearing failures accounting for a substantial proportion (40$\%$ to 90$\%$) of all such failures. To address this issue, intelligent algorithms have been developed to evaluate vibrational signals and accurately detect faults, thereby reducing the reliance on expert knowledge and lowering maintenance costs. Within the field of machine learning, Artificial Immune Systems (AIS) have exhibited notable potential, with applications ranging from malware detection in computer systems to fault detection in bearings, which is the primary focus of this study. In pursuit of this objective, we propose a novel procedure for detecting novel instances of anomalies in varying operating conditions, utilizing only the signals derived from the healthy state of the analyzed machine. Our approach incorporates AIS augmented by Dynamic Time Warping (DTW). The experimental outcomes demonstrate that the AIS-DTW method yields a considerable improvement in anomaly detection rates (up to 53.83$\%$) compared to the conventional AIS. In summary, our findings indicate that our method represents a significant advancement in enhancing the resilience of AIS-based novelty detection, thereby bolstering the reliability of rotating machines and reducing the need for expertise in bearing fault detection.
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.
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).
Ghulam Farid,Sidra Bibi,Laxmi Rathour,Lakshmi Narayan Mishra,Vishnu Narayan Mishra 강원경기수학회 2023 한국수학논문집 Vol.31 No.1
We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly $(s,m)$-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.
FIXED POINTS OF MULTI-VALUED OSILIKE-BERINDE NONEXPANSIVE MAPPINGS IN HYPERBOLIC SPACES
Kiran Dewangan,Niyati Gurudwan,Laxmi Rathour 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.3
This paper is concerned with fixed point results of a finite family of multi-valued Osilike-Berinde nonexpansive type mappings in hyperbolic spaces along with some numerical examples. Also strong convergence and $\Delta-$convergence of a sequence generated by Alagoz iteration scheme are investigated.