Research Article
African Journal of Mathematics and Mathematical Sciences ISSN: 3821-435x Vol. 2 (2), pp. 038-046, February, 2013. © International Scholars Journals
Full Length Research Paper
Coupled fixed points results for W-Compatible Maps in symmetric G-Metric spaces
Sumitra Dalal1 and Dimplekumar Chalishajar2
1College of Science, Jazan University, K.S.A. Saudi Arabia.
2 Department of Applied Mathematics, Mallory hall, Virginia Military Institute, VA 24450, USA.
Corresponding author. E-mail: [email protected],Phone: 1-540-817-8105
Accepted 31 October, 2013
Abstract
Mustafa,(2004) generalized the concept of metric spacesby introducing G-metric spacesand proved fixed point theorems for maps satisfying different contractive conditions[see Mustafa,(2004),(2006),(2008),(2009),(2010)]. In this article, we introduce the notion of w-compatible maps, b-coupled coincidence points and b-common coupled fixed points for non self maps and obtain fixed point results using these new notions in G-metric spaces. It is worth to mention that our results neither rely on completeness of the space nor the continuity of any mappings involved therein. Also, relevant examples have been cited to illustrate the effectiveness of our results. As an application,we demonstrate the existence of solution of system of nonlinear integral equations.
Key words: Coupled fixed point, w- compatible maps,G-metric spaces, Integral equations.
Sumitra Dalal, Dimplekumar Chalishajar
Page: 38 - 46
Research Article
African Journal of Mathematics and Mathematical Sciences ISSN: 3821-435x Vol. 2 (1), pp. 023-037, January, 2014. © International Scholars Journals
Full Length Research Paper
Christ-Obimba tangent, permutation, sequence and series rules in Calculus
Obimba Kelechukwu Clarence
Department of Biochemistry, School of Science, Federal University of Technology Owerri, P.M.B. 1526, Owerri. Nigeria. E-mail: [email protected]; Tel. 07034851899
Accepted 02 January, 2014
Abstract
The aim of this study is to develop a convenient Tangent rule that could be used for determining the area and lengths of sides of a triangle, and also to develop differentiation and integral calculus rules/formulae based on permutation and geometric progression. Christ-Obimba Calculus Rule 1 could be used in determining further/higher derivatives of a function, directly from the parent function, without recourse to the consecutive, previous derivative. For any triangle ( ) ABC,
, , and .
a, b, and c are lengths of the sides of the triangle( ) ABC (Christ-Obimba Tangent Rules).
known as Christ-Obimba Calculus Rules 1 and 2, respectively, could be used in calculus of differentiation, for determining derivatives, and further derivatives of mathematical functions. Parent /root mathematical functions, their consecutive derivatives, and further/higher derivatives, form the Christ-Obimba geometric progression sequence in calculus, given by :
The Christ-Obimba geometric progression series in calculus could be used to obtain all the derivatives, of the parent function of a finite series, without calculating individual derivatives, singly.
m = the specific derivative (1st, or 2nd or 3rd…….or mth derivative).
n = index power to which the variable x is raised. e.g : x4 (n = 4).
a = constant = coefficient of the variable term in xn.
C = constant.
T1 =the first term of the geometric progression series of calculus = axn.
Ti = the dependent variable y; Td = the term in the independent variable x.
Key Words: Tangent, calculus, permutation, geometric progression series, derivatives.
Obimba Kelechukwu Clarence
Page: 23 - 37
Research Article
African Journal of Mathematics and Mathematical Sciences Vol. 2 (1), pp. 013-015, January, 2014. © International Scholars Journals
Full Length Research Paper
Conjugate gradient method for non-positive definite matrix operator
Omolehin J.O.1*, Abdulrahman M.K.A.1, Rauf K.1and Udoh P.J. 2
1Mathematics Department, University of Ilorin, Ilorin, Nigeria.
2Mathematics Department, University of Uyo, Uyo, Nigeria.
*Corresponding author. E-mail: [email protected]
Accepted 18 September, 213
Abstract
The conjugate Gradient Method relies on symmetric positive definite property of a matrix operator. In this work, we investigate and establish the case of non-positive symmetric matrix operator using various forms of conversions and transformations on the operator.
Key words: Hilbert Space, Positive Symmetric Matrix, Quadratic Functional, Conjugate, Gradient Method.
Abdulrahman M.K.A., Rauf K. and Udoh P.J., Omolehin J.O.*
Page: 13 - 15
Research Article
African Journal of Mathematics and Mathematical Science Vol. 1 (1), pp. 001-012, October, 2013. © International Scholars Journals
Full Length Research Paper
Weak Contractions for Coupled Fixed Point Theorem on G-metric space
Animesh Gupta
Department of Mathematics Sagar Institute of Science, Technology & Research, Ratibad Bhopal, India.
E-mail: [email protected]
Accepted 9 August, 2013
Abstract
In recent time, fixed point theory has been developed rapidly in partially ordered metric space. Bhaskar and Lakshmikantham (2006) introduced the concept of mixed monotone property. Lakshmikanthem and Ciric (2009) generalized the concept of mixed monotone mapping and proved a common coupled fixed point theorem. In this paper, we find a new type of contractive condition on G- metric spaces also the purpose of this paper is to generalized some recent coupled fixed point theorems in G- metric spaces. We further give some concrete examples in order to support our main theorems. The obtained results generalize those announced by many authors also the main result in this paper is the following coincidence point theorem which generalizes Theorems of Z. Mustafa, W. Shatanawi and M. Bataineh (2008)[13] Z. Mustafa, W. Shatanawi and M. Bataineh (2009)[14], Z. Mustafa and B. Sims, (2009)[15], H.K. Nashine,(2012)[16], W. Shatanawi, S. Chauhan, M. Postolache, M., Abbas and S. Radenović (2013)[17], R.Wangkeeree, Bantaojai (2012)[18].
Subject classification [2000]: 54H25, 46J10
Keywords: G- metric spaces, ordered set, coupled coincidence point, coupled common fixed point, mixed monotone.
Animesh Gupta
Page: 1 - 12