<p>This paper introduces the concept of D-symmetric spaces, a new class of strong distance spaces, and investigates their role in the construction of fractals. To address challenges arising from fractal generation under non conventional contraction conditions, we establish the existence of attractors for mappings satisfying Reich–Chatterjea type contractions within this newly developed framework. We further extend the theory of iterated function systems by proposing Reich–Chatterjea Iterated Function Systems (RC-IFS) and Cyclic Reich–Chatterjea Iterated Function Systems (CRC-IFS), thereby accommodating a wider range of contraction mappings. These developments offer a robust foundation for studying fractals in generalized metric spaces and open new pathways for applications in analysis and dynamical systems. Overall, the results significantly advance the understanding of non conventional contractions and broaden the scope of fixed point theory in fractal generation under strong distance structures.</p>

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D-Symmetric Space: A New Approach to Non Conventional Attractors

  • Kifayat Ullah,
  • S. K. Katiyar,
  • Maha Noorwali

摘要

This paper introduces the concept of D-symmetric spaces, a new class of strong distance spaces, and investigates their role in the construction of fractals. To address challenges arising from fractal generation under non conventional contraction conditions, we establish the existence of attractors for mappings satisfying Reich–Chatterjea type contractions within this newly developed framework. We further extend the theory of iterated function systems by proposing Reich–Chatterjea Iterated Function Systems (RC-IFS) and Cyclic Reich–Chatterjea Iterated Function Systems (CRC-IFS), thereby accommodating a wider range of contraction mappings. These developments offer a robust foundation for studying fractals in generalized metric spaces and open new pathways for applications in analysis and dynamical systems. Overall, the results significantly advance the understanding of non conventional contractions and broaden the scope of fixed point theory in fractal generation under strong distance structures.