FIXED POINT THEOREMS FOR NONLINEAR CONTRACTIONS IN ORDERED PARTIAL METRIC SPACES

BINAYAK S.  CHOUDHURY; AMARESH  KUNDU

FIXED POINT THEOREMS FOR NONLINEAR CONTRACTIONS IN ORDERED PARTIAL METRIC SPACES

Authors

BINAYAK S. CHOUDHURY Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O - B. Garden, Howrah - 711103, India
AMARESH KUNDU Department of Mathematics, Siliguri Institute of Technology, P.O - Sukna, Darjeeling - 734009, WestBengal, India

Keywords:

Partially ordered set, Partial metric, Non-decreasing mapping, Weak contraction, Control functions, Fixed point

Abstract

In this paper we develope the weak contraction mapping principle in the context of partial metric spaces which are generalizations of metric spaces meant for the study of denotational semantics of programming languages. We consider certain control conditions for this purpose and accomplish the task in partial metric spaces. Additionally, a partial order is defined on this space. An illustrative example is given. The method we use in this paper is a combination of analytic and order theoretic methodologies.