GENERAL MATHEMATICS NOTES

Vol. 4, No. 1, May 2011 

Contents

Title: Some Results on Intuitionistic Fuzzy Ideals in BCK-Algebras

Authors: B. Satyanarayana and R. Durga Prasad

Abstract: In this paper, we give some results on the intuitionistic fuzzy implicative ideals, intuitionistic fuzzy positive implicative ideals, intuitionistic fuzzy commutative ideals.

PP. 1-15

Title: Variational Discretization and Mixed Methods for Semilinear Parabolic Optimal Control Problem

Author: Zuliang Lu

Abstract: In this paper we study the variational discretization and mixed finite element methods for optimal control problem governed by semilinear parabolic equations. The space discretization of the state variable is done using usual mixed finite elements. The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Then we derive a priori error estimates both for the coupled state and the control approximation.

PP. 16-27

Title: Unique Fixed Point Theorem for Weakly S-Contractive Mappings

Authors: D.P. Shukla and Shiv Kant Tiwari

Abstract: In this paper, we have unique fixed point theorem using S-contractive mappings in complete metric space. We supported our result by some examples.

PP. 28-34

Title: Subdivisions of the Spectra for the Triple Band Matrix over Certain Sequence Spaces

Authors: Feyzi Başar, Nuh Durna and Mustafa Yildirim

Abstract: In a series of papers, B. Altay, F. Başar and A.M. Akhmedov recently investigated the spectra and fine spectra for difference operator, considered as bounded operator over various sequence spaces. In the present paper approximation point spectrum, defect spectrum and compression spectrum of an operator represented by the triple band matrix B(r,s,t) over the sequence spaces c₀, c, ℓ_p and bv_p are determined, where bv_p denotes the space of all sequences x_k such that (x_k –x_k-1) belongs to the sequence space ℓ_p with 1≤p≤∞ and was studied by Başar and Altay [Ukrainian Math. J., 55(1) (2003), 136-147].

PP. 35-48

Title: Supplier Selection Strategies on Fuzzy Decision Space

Author: M. Pattnaik

Abstract: Supplier selection is a major strategy for manufacture to run the production process smoothly. Supplier categorization, selection and performance evaluation are decisions of strategic importance to companies. Global competition, mass customization, high customer expectations and harsh economic conditions are forcing companies to rely on external suppliers to contribute a larger portion of parts, materials, and assemblies to finished products and to manage a growing number of processes and functions that were once controlled internally. Thus supplier performance evaluation is very important to choose the right supplier for the right product. In this paper a fuzzy supplier selection algorithm (FSSA) is implemented to rank the technically efficient vendors according to both predetermined performance criteria and additional product-related performance criteria. Investigation of the properties of the best supplier alternative by ranking the fuzzy indices allow to develop an algorithm which is based on calculating fuzzy suitability indices for the efficient supplier alternatives and validity is illustrated through an example problem.

PP. 49-69

Title: Properties of Contra sg-Continuous Maps

Authors: O. Ravi,  M. Lellis Thivagar and R. Latha

Abstract: In [Dontchev J. Contra-continuous functions and strongly S-closed spaces.  Int. J. Math. Math. Sci. 1996; 19(2):303-310], Dontchev introduced and investigated a new notion of continuity called contra-continuity. Following this, many authors introduced various types of new generalizations of contra-continuity called contra-a-continuity [22], contra-semi-continuity [7], contra precontinuity [21],  contra-super-continuity [23], contra-b-continuity [3], almost-contra-super-continuity [14], contra-d-precontinuity [11], almost-contra-precontinuity [12] and contra sg-continuity [7] and so on [13 and 33].  In this paper, we investigate a generalization of contra-continuity by utilizing semi-generalized closed sets [1].

PP. 70-84

Title: On Power Г-Semigroups

Author: Thawhat Changphas

Abstract: Let S₁ and S₂ be Г-semigroups. In this note, we determine when S₁ and S₂ are isomorphic if the power semigroup of S₁ and the power semigroup of S₂ are o-isomorphic.

PP. 85-89 

Title: New Perspectives on CDPU Graphs

Authors: Beena Koshy and Germina K.A.

Abstract: A graph G = (V, E) is Complementary Distance Pattern Uniform if there exists M subset of V(G) such that ƒ_M(u) = {d(u, v) : v in M}, for every u  belongs to V(G)-M, is independent of the choice of u in V(G)-M and the set M is called the Complementary Distance Pattern Uniform Set (CDPU set). In this paper, we initiate a study on the CDPU sets of trees.

PP. 90-98