GENERAL MATHEMATICS NOTES

Vol. 7, No. 2, December 2011 

Contents

Title: Generalized Intuitionistic Fuzzy Soft Sets and its Applications

Authors: Babitha K V and Sunil Jacob John

Abstract: In this paper we define generalized intuitionistic fuzzy soft sets and set theoretical operations with illustrating examples. It also proposes a similarity measure for generalized intuitionistic fuzzy soft set and used it to find out the similarity between synthetic texture and natural texture. A congenial method for solving multi criteria decision making problem in generalized intuitionistic fuzzy soft set frame work is presented.

PP. 1-14

 Title: Products of Menger Probabilistic Normed Spaces

 Authors: K.P.R.Sastry, G.A.Naidu, V. Madhavi Latha, S.S.A.Sastri and I. Laxmi Gayatri

 Abstract: In this paper, we study Menger Probabilistic Normed (PN) spaces in a detailed way; we introduce the notation of a finite product of Menger Probabilistic Normed spaces, show that a finite product of complete Menger probabilistic normed spaces is itself complete and every Cauchy sequence in a Menger probabilistic normed space is norm totally bounded under certain conditions. We also introduce the notion of L-Menger PN spaces and show that in a L-Menger PN space $(X, \tilde{F}, *)$, the distribution map $\tilde{F}$ determines and is determined by a single distribution function on R.

PP. 15-23

 Title: A Fixed Point Theorem for Six Mappings in Metric Space

 Authors: Rajesh Shrivastava, Sarvesh Agrawal, Ramakant Bhardwaj and R.N. Yadava

 Abstract: In present paper we prove a common fixed point theorem for six mappings using compatibility, weak compatibility and commutativity. Our results improve one of the result of Imdad and Khan [3], fisher [2].

PP. 24-37

 Title: A Fixed Point Theorem in Cone Metric Spaces under Weak Contractions

 Authors: K. P. R. Sastry, Ch. Srinivasa Rao, A. Chandra Sekhar and M. Balaiah

 Abstract: In this paper, we improve the result of B.S. Choudhury and N. Metiya, Nonlinear Analysis 72 (2010). We remove the restriction of continuity on φ. Supporting examples are also provided. Two open problems are given at the end.

PP. 38-44

Title: The Strongly Summable Generalized Difference Double Sequence Spaces in 2-Normed Spaces Defined by an Orlicz Function

Authors: Vakeel A. Khan and Sabiha Tabassum

Abstract: The main aim of this paper is to introduce a new class of sequence spaces namely $_{2}V^{\bar{\lambda}}[A,\Delta_{(mv)}^n, M, p, \|.,.\|]_\sigma$ where σ = 0, 1, ∞ using the concept of 2-norm and the notion of de la Valee-Pousin means when $A = (a_{m,n,j,k)}$, j, k = 0,1,... is a doubly infinite matrix of real numbers for all m, n = 0,1,.... To construct these spaces we use an Orlicz function, a bounded sequence of positive real numbers and a generalized difference operator which was introduced by Dutta[2] . We obtain various inclusion relations involving these sequence spaces.

PP. 45-58

Title: m-Systems and n-Systems in Ordered Ternary Semigroups

Author: Thawhat Changphas

Abstract: In this note, the concepts of m-systems and n-systems in ordered ternary semigroups will be introduced and studied.

PP. 59-62