Some Meir – Keeler and Integral

Some Meir – Keeler and Integral Type Fixed Point Theorems in Dislocated Metric Space


by Dr. Disha Madan(Author)

ISBN Number : 978- 1-63042- 052-8

SKU: SBP_1642 Category:


Dr. Dinesh Panthi
Dr. Dinesh Panthi, (Ph.D. from Kathmandu University, Nepal in 2013)
Associate Professor, Department of Mathematics, Valmeeki Campus, Nepal
Sanskrit University, Nepal. Dr. Panthi has published more than three dozen
research articles in various reputed journals in the field of fixed point theory
and its applications. Major research works are in the field of Dislocated
Metric Space and Dislocated Quasi Metric Spaces

1.1 Introduction
Fixed point theory is an important area of nonlinear functional analysis. In 1922, S. Banach
[11] established a fixed point theorem in complete metric space, which is famous as Banach
contraction principle. In 1969, A. Meir and E. Keeler [4] obtained a remarkable
generalization of Banach Contraction principle with the notion of weakly uniformly strict
contraction which is famous as (  ) contraction principle. Since then, many authors
havegeneralized and extended Meir- Keeler type fixed point results in metric space.
In 1976. G. Jungck [6] initiated the concept of commuting maps and generalized it with the
concept of compatible maps [7, 8] and established some important common fixed point
theorems. In 1999, R.P.Pant [10] introduced the concept of reciprocally continuous mappings
and established common fixed point theorems in metric space.
In 2000 P. Hitzler and A.K. Seda [9] initiated the concept of dislocated topology in which the
dislocated metric space is obtained. Dislocated metric plays very important role in Topology,
semantics of logic programming and in electronics engineering.
The purpose of this chapter is to establish some Meir-Keeler type common fixed point
theorems using compatibility and reciprocal continuity of mappings in complete dislocated
metric space.