GENERAL MATHEMATICS NOTES

Vol. 6, No. 2, October 2011 

Contents

Title: A Note on the Relation between Potential Terms and Metric Matrices

Authors: Yuya Dan

Abstract: The purpose of this paper is to introduce representation of kinetic fields in Schrödinger equations and to give the relation between potential terms and metric matrices via general structure of spaces rather than Euclidean spaces. We obtain two results from the point of view in Fourier analysis and pseudodifferential operators. One is the derivation of the potential terms in Schrödinger equations from the representation of kinetic fields by metric matrices in Schrödinger type equation, the other is the derivation the metric matrices in Schrödinger type equation from the potential terms in Schrödinger equation in the one-dimensional Euclidean space.

PP. 1-11

Title: Common Fixed Point for a Pair of Self-Maps Satisfying the Property E. A.

Author: T. Phaneendra

Abstract: Using the notion of contractive modulus, we obtain a common fixed point for a pair of weakly compatible self-maps on a metric space, which satisfy the property E.A. Eventually our result is a modest generalization of an earlier result of the author. We also show that a common fixed point can be obtained from this result through the notions of compatibility and reciprocal continuity. In the linear setting of our second result, we get those of Rangamma et al as particular cases.

PP. 12-18

Title: A Generalization of Badshah and Singh’s Result through Compatibility

Authors: T. Phaneendra and M. Chandra Shekhar

Abstract: Using the idea of compatibility of self-maps, due to Gerald Jungck, we obtain a modest generalization of Badshah and Singh’s result.

PP. 19-23

Title: On Degree of Approximation by Product Means (E, q)(N, P_n) of Fourier Series

Authors: Mahendra Misra,U. K. Misra,B. P. Padhy and M. K. Muduli

Abstract: In this paper a theorem on degree of Approximation of a function f belongs to     Lip α by product summability  (E, q)(N, P_n) of Fourier series associated with f.

PP. 24-32

Title: On Lacunary Strongly Convergent Difference Sequence Spaces Defined by a Sequence of  φ-Functions

Authors: Metin Başarir and Selma Altundağ

Abstract: In this paper, we introduce the new sequence spaces with lacunary strong convergence using by a sequence of modulus functions and a sequence of φ-functions. We also study some connections between lacunary (A, φ_k, Δ^m_u) - statistically convergence and lacunary strong (A, φ_k, Δ^m_u) - convergence.

PP. 33-44

Title: Multipoint Algorithms Arising from Optimal in the Sense of Kung-Traub Iterative Procedures for Numerical Solution of Nonlinear Equations

Authors: Boryana Ignatova, Nikolay Kyurkchiev and Anton Iliev

Abstract: In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of effciency in the sense of Ostrowski - Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations (method regula falsi, modifications of Euler - Chebyshev method, Halley method, and others) due to optimal in the sense of the Kung-Traub algorithm of order 4 and 8. Some hypothetical iterative procedures generated by algorithms from order of convergence 16 and 32 are also studied (the receipt and publication of which is a matter of time, having in mind the increased interest in such optimal algorithms). The corresponding model theorems for their convergence speed and effciency index have been formulated and proved.

PP. 45-79

Title: On Some New Almost Double Lacunary Δ^m-Sequence Spaces Defined by Orlicz Functions

Authors: Vakeel A. Khan and Sabiha Tabassum

Abstract: In this paper we introduce a new concept for almost double lacunary Δ^m- sequence spaces defined by Orlicz function and give inclusion relations. The results here in proved are analogous to those by Ayhan Esi [General Mathematics (2009), 2(17) 53-66] .

PP. 80-94