A Common Fixed Point Theorem for Generalised F -Kannan Mapping in Metric Space with Applications

This paper is aimed at proving a common fixed point theorem for F -Kannan mappings in metric spaces with an application to integral equations. The main result of the paper will extend and generalise the recent existing fixed point results in the literature. We also provided illustrative examples and some applications to integral equation, nonlinear fractional differential equation, and ordinary differential equation for damped forced oscillations to support the results.

Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space

In the article the concept of metric space could be expanded, one of which is a partial metric space. In the metric space, the distance of a point to itself is equal to zero, while in the partial metric space need not be equal to zero.The concept of partial metric space is used to modify Banach's contraction principle. In this paper, we discuss weakly contractive mapping and weakly Kannan mapping which are extensions of Banach's contraction principle to partial metric space together some related examples. Additionally, we discuss someLemmas which are shows an analogy between Cauchy sequences in partial metric space with Cauchy sequences in metric space and analogy between the complete metric space and the complete partial metric space. Keywords: Cellulose metric space, partial metric space, weakly contraction mapping, weakly Kannan mapping.

WEAKLY CONTRACTIVE MAPPING IN PARTIAL METRIC SPACE

Contractive mapping is one kind of mapping that guarantees a fixed point in a metric space Many experts has developed this kind of mapping to show the existence of a fixed point such as Kannan mapping and Chatterjea Contractive mapping. In this study, we will show the weakly contractive mapping to show the existence of fixed point in the partial metric space

Some fixed point theorems for Kannan mapping in the modular spaces

In this article, a new version of Kannan mapping theorem in modular space is presented. The main result of this paper is the existence of fixed point of Kannan mapping in complete modular spaces that have Fatou property.

K-ITERATED FUNCTION SYSTEM

In 1969, Kannan1 gave the definition of a new mapping which had presented a condition which is more lenient than contraction condition. The purpose of this note is to introduce K-Iterated Function System using Kannan mapping which will cover a larger range of mappings. We also prove the Collage theorem for the K-Iterated Function System.

TEOREMA TITIK TETAP UNTUK PEMETAAN KANNAN PADA RUANG METRIK MODULAR TERITLAK

In this paper, we will discuss about fixed point theorems in generalized modular metric space for Kannan- type mapping. The existence of the fixed point of this mapping is guaranteed by providing that the mapping domain is a -finite set and the Kannan- mapping constant satisfied where K is a constant from the axiom of generalized modular metric space.