**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3

# metric space Related Publications

##### 3 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces

**Authors:**
Ismat Beg,
Asma Rashid Butt

**Abstract:**

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

**Keywords:**
Fixed Point,
metric space,
partially ordered set,
set
valued mapping

##### 2 A New Class χ2 (M, A,) of the Double Difference Sequences of Fuzzy Numbers

**Authors:**
N.Subramanian,
U.K.Misra

**Abstract:**

The aim of this paper is to introduce and study a new concept of strong double χ2 (M,A, Δ) of fuzzy numbers and also some properties of the resulting sequence spaces of fuzzy numbers were examined.

**Keywords:**
fuzzy number,
Modulus function,
metric space

##### 1 A New Class F2 (M, 0, N)L„ p)F of The Double Difference Sequences of Fuzzy Numbers

**Authors:**
N. Subramanian,
C. Murugesan

**Abstract:**

The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.

**Keywords:**
metric space,
Orlicz function,
solid space,
completeness