Bijendra Singh

Common fixed points of compatible maps in fuzzy metric spaces

The purpose of this paper is to introduce the concept of compatibility in fuzzy metric space and prove two common fixed point theorems illustrating with an example.

Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation

The concept of semicompatibility has been introduced in fuzzy metric space and it has been applied to prove results on existence of unique common fixed point of four self-maps satisfying an implicit relation. Recently, Popa (2002) has employed a similar but not the same implicit relation to obtain a fixed point theorem for d-complete topological spaces. All the results of this paper are new.

Fixed points of associated multimaps of fuzzy maps

In this paper we prove some results for associated multimaps of fuzzy maps taking a new inequality initiated by Ray (1988).

Semicompatibility and fixed point theorems in an unbounded D-metric space

Rhoades (1996) proved a fixed point theorem in a bounded D-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded D-metric space, for two self-maps satisfying a general contractive condition with a restricted domain of x and y. This has been done by using the notion of semicompatible maps in D-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory of D-metric spaces. All the results of this paper are new.

On the Products of -Fibonacci Numbers and -Lucas Numbers

In this paper we investigate some products of -Fibonacci and -Lucas numbers. We also present some generalized identities on the products of -Fibonacci and -Lucas numbers to establish connection formulas between them with the help of Binets formula.