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Fractal Fract
Volume 10
Issue 7
10.3390/fractalfract10070433
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces

by
Loitongbam Melei Singh
1,
Yumnam Rohen
1,
Thangjam Bimol
2,
Naeem Saleem
3,4 and
Mahpeyker Öztürk
5,6,*
1
Department of Mathematics, Manipur University, Canchipur, Imphal 795003, India
2
Department of Mathematics, Jadonang Memorial College, Noney 795159, India
3
Department of Mathematics, University of Management and Technology, Lahore 54770, Punjab, Pakistan
4
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa 0208, Gauteng, South Africa
5
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Türkiye
6
Picode Software, Education Training Consultancy Research and Development and Trade Co., Ltd., Sakarya 54050, Türkiye
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(7), 433; https://doi.org/10.3390/fractalfract10070433 (registering DOI)
Submission received: 12 May 2026 / Revised: 3 June 2026 / Accepted: 5 June 2026 / Published: 25 June 2026
(This article belongs to the Special Issue Fixed Point Methods for Fractional Differential and Integral Equations)
Versions Notes

Abstract

In this paper, we introduce the concept of a (λσ,ϖ1σ,ϖ2σ)-interpolative Ćirić–Reich–Rus contraction iterated function system and an iterated multivalued system using interpolative Ćirić–Reich–Rus operators. The objective of this paper is to construct fractals using the Hutchinson operator and Hutchinson-like operator involving interpolative Ćirić–Reich–Rus contraction mappings, which extend the class of classical contractions, in b-metric space. The use of interpolative Ćirić–Reich–Rus contraction guarantees unique fractal attractors, thereby playing a vital role in the analysis of geometric structures and their wide-range applications in scientific and engineering fields. Using the above new definitions, we present a version of the Collage theorem adapted to iterated function systems satisfying interpolative Ćirić–Reich–Rus contractions. Further, we study the well-posedness of the new interpolative Ćirić–Reich–Rus contraction-iterated function system-Hutchinson problem. Our findings unify, generalize, and extend various earlier results reported in the literature.
Keywords: fractals; attractor; fixed point; interpolative Ćirić–Reich–Rus mapping; b-metric space; Hutchinson operator fractals; attractor; fixed point; interpolative Ćirić–Reich–Rus mapping; b-metric space; Hutchinson operator

Share and Cite

MDPI and ACS Style

Singh, L.M.; Rohen, Y.; Bimol, T.; Saleem, N.; Öztürk, M. Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces. Fractal Fract. 2026, 10, 433. https://doi.org/10.3390/fractalfract10070433

AMA Style

Singh LM, Rohen Y, Bimol T, Saleem N, Öztürk M. Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces. Fractal and Fractional. 2026; 10(7):433. https://doi.org/10.3390/fractalfract10070433

Chicago/Turabian Style

Singh, Loitongbam Melei, Yumnam Rohen, Thangjam Bimol, Naeem Saleem, and Mahpeyker Öztürk. 2026. "Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces" Fractal and Fractional 10, no. 7: 433. https://doi.org/10.3390/fractalfract10070433

APA Style

Singh, L. M., Rohen, Y., Bimol, T., Saleem, N., & Öztürk, M. (2026). Some Fixed Point Results for Fractals of Interpolative Ćirić–Reich–Rus Mappings in b-Metric Spaces. Fractal and Fractional, 10(7), 433. https://doi.org/10.3390/fractalfract10070433

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