The Journal of the Indian Mathematical Society

Arun Kumar ¹, V. N. Jha ²

Affiliations
1 Department of Mathematics, Rani Durgavati University, Jabalpur–482001, IN
2 Department of Mathematics, Galgotia’s College of Engineering, Greater Noida–201306, IN

Abstract

In this paper, we obtain a precise estimate for the quartic spline interpolating the second derivatives at the knots and the functional values at the mid points of the knots.

Keywords

Interpolation, Quartic Spline, DeCient, Error Bounds.

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Arun Kumar ¹, Karun Lata Shukla ¹

Affiliations
1 Department of Mathematics and Computer Science, R. D. University, Jabalpur (M.P.), IN

Abstract

There has been study on inclusion relation of (N, p_n) and (N̅, p_n): The inclusion relations in the sense of totally stronger of these methods were obtained by Kuttner and Rhoades. We study totally stronger inclusion relation of product methods.

Keywords

Matrix Methods, Inclusion Relation, Totally Stronger, Product Methods.

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Arun Kumar ¹, G. V. Prasad ¹

Affiliations
1 Department of Mathematics, University of Jabalpur, Jabalpur, IN

Abstract

A matrix A is called (f) or (F) - efifective if the Fourier series of f(x), satisfying the condition that

Φ(t) = i {f ( x + t) + (x - t) - 2l} → 0

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Manprit Kaur ¹, Arun Kumar ¹

Affiliations
1 Department of Mathematics and Computer Science, R.D. University, Jabalpur (M.P)-482 001, IN

Abstract

The study of cubic splines and deficient cubic splines interpolating at intermediate points including nodal points was made in [3], [5], [6] and [7]. The complex cubic splines were considered in [1] and [2]. The deficient complex cubic spline function interpolating at the nodal points of subarcs of a rectifiable Jordan are was considered by Chatterjee and Dikshit [4]. In the present paper we consider a natural question whether the deficient complex cubic spline function can be obtained which interpolates at an intermediate point of the subarcs including nodal points. We show that the analysis of the paper [4] can be extended to establish that interpolations at intermediate points are possible.

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