Work

Fractals of Interpolative Kannan Mappings

Year: 2024

Type: article

Abstract: In 2018, Erdal Karapinar introduced the concept of interpolative Kannan operators, a novel adaptation of the Kannan mapping originally defined in 1969 by Kannan. This new mapping condition is more lenient than the basic contraction condition. In this paper, we study the concept by introducing the IKC-iterated function/multi-function system using interpolative Kannan operators, including a broader area of mappings. Moreover, we establish the Collage Theorem endowed with the iterated function system (IFS) based on the IKC, and show the well-posedness of the IKC-IFS. Interpolative Kannan contractions are meaningful due to their applications in fractals, offering a more versatile framework for creating intricate geometric structures with potentially fewer constraints compared to classical approaches.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract8080493

Authors: Xiangting Shi, Umar Ishtiaq, Muhammad Din, Mohammad Akram

Institutions: Columbia University, Quaid-i-Azam University, Thammasat University, Islamic University of Madinah

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,069

Funder: Islamic University of Madinah