arXiv subjects

D. Ramesh Kumar

Publications and source records attributed to D. Ramesh Kumar.

2 recordsLinked to original sources

arXiv2023

Generalized Proinov-type contractions using simulation functions with applications to fractals

The intention of this article is to introduce a generalization of Proinov-type contraction via simulation functions. We name this generalized contraction map as Proinov-type Z-contraction. This article establishes the existence and uniqueness of fixed points for these contraction mappings in quasi-metric space and also, include explanatory examples with graphical interpretation. As an application, we generate a new iterated function system (IFS) consisting of Proinov-type Z-contractions in quasi-metric spaces. At the end of the paper, we prove the existence of a unique attractor for the IFS consisting of Proinov-type Z-contractions.

math.FA↗

arXiv2023

Some Coupled Fixed Point Theorems for (\psi, \phi)- contraction with Applications to Fractals

In this paper, we obtain coupled fixed point theorem for (\psi, \phi)-contractions under some generalized conditions on the real valued functions \psi and \phi defined on (0,\infinity). Also, we present a generalized version of coupled fixed point theorem for the same (\psi, \phi)- contractions. A new approach to fractal generation using the relation between fractals and fixed points is given in light of these fixed point theorems. We establish a new type of iterated function system consisting of generalized (\psi, \phi)-contractions. We also extend those results to coupled fractals.

math.FA↗