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2: Paper Source PDF document

Paper's Title:

A New Relaxed Complex-valued b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and T. C. M. Jele

Department of Mathematics, University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za
singhv@ukzn.ac.za
thokozani.jele@nwu.ac.za

Abstract:

In this paper, we study the existence and uniqueness of fixed point in complex valued b-metric spaces and introduce a new relaxed α, β Complex-valued b-metric type by relaxing the triangle inequality and determine whether the fixed point theorems are applicable in these spaces.



2: Paper Source PDF document

Paper's Title:

A Generalization of a Partial b-metric and Fixed Point Theorems

Author(s):

Pravin Singh and Virath Singh

Department of Mathematics, University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za
singhv@ukzn.ac.za

Abstract:

The purpose of this paper is to introduce the concept of a Partial α, β b-metric as a generalization of a partial b-metric and prove theorems for some contractive type mapping.



1: Paper Source PDF document

Paper's Title:

Oblique Projectors from the Simpson Discrete Fourier Transformation Matrix

Author(s):

P. Singh and V. Singh

School of Mathematics, Computer Science and Statistics,
University of Kwazulu-Natal,
Private Bag X54001, Durban 4001,
South Africa.
E-mail: singhp@ukzn.ac.za, singhv@ukzn.ac.za

Abstract:

In this paper we examine the projectors of the Simpson Discrete Fourier Transform matrix of dimension two modulus four and show how they decompose the complex vector space into a direct sum of oblique eigenspaces. These projection operators are used to define a Simpson Discrete Fractional Fourier Transform (SDFRFT).



1: Paper Source PDF document

Paper's Title:

A New Relaxed b-metric Type and Fixed Point Results

Author(s):

P. Singh, V. Singh and Thokozani Cyprian Martin Jele

Department of Mathematics,
University of KwaZulu-Natal,
Private Bag X54001, Durban,
South Africa.
E-mail: singhp@ukzn.ac.za, singhv@ukzn.ac.za, thokozani.jele@nwu.ac.za

Abstract:

The purpose of this paper is to introduce a new relaxed α, β b-metric type by relaxing the triangle inequality. We investigate the effect that this generalization has on fixed point theorems.



1: Paper Source PDF document

Paper's Title:

Orthogonal Collocation on Finite Elements Using Quintic Hermite Basis

Author(s):

P. Singh, N. Parumasur and C. Bansilal

University of KwaZulu-Natal,
School of Mathematics Statistics and Computer Sciences,
Private Bag X54001,
Durban, 4000,
South Africa.
E-mail: singhprook@gmail.com
parumasurn1@ukzn.ac.za
christelle18@gmail.com

Abstract:

In this paper we consider the orthogonal collocation on finite elements (OCFE) method using quintic Hermite (second degree smooth) basis functions and use it to solve partial differential equations (PDEs). The method is particularly tailored to solve third order BVPS and PDEs and to handle their special solutions such as travelling waves and solitons, which typically is the case in the KdV equation. The use of quintic polynomials and collocation using Gauss points yields a stable high order superconvergent method. OCFE using quintic Hermite basis is optimal since it is computationally more efficient than collocation methods using (first degree smooth) piecewise-polynomials and more accurate than the (third degree smooth) B-splines basis. Various computational simulations are presented to demonstrate the computational efficiency and versatility of the OCFE method.


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