POLYNOMIOGRAPHS AND CONVERGENCE: A COMPARATIVE STUDY OF ITERATION PROCESSES UNDER KANANN-SUZUKI-(C) CONDITION

Bashir Nawaz; Kifayat Ullah; Hasanen A. Hammad; Manuel De la Sen

doi:10.11948/20240236

2025 Volume 15 Issue 5

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Bashir Nawaz, Kifayat Ullah, Hasanen A. Hammad, Manuel De la Sen. POLYNOMIOGRAPHS AND CONVERGENCE: A COMPARATIVE STUDY OF ITERATION PROCESSES UNDER KANANN-SUZUKI-(C) CONDITION[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2528-2550. doi: 10.11948/20240236

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Bashir Nawaz, Kifayat Ullah, Hasanen A. Hammad, Manuel De la Sen. POLYNOMIOGRAPHS AND CONVERGENCE: A COMPARATIVE STUDY OF ITERATION PROCESSES UNDER KANANN-SUZUKI-(C) CONDITION[J]. Journal of Applied Analysis & Computation, 2025, 15(5): 2528-2550. doi: 10.11948/20240236

POLYNOMIOGRAPHS AND CONVERGENCE: A COMPARATIVE STUDY OF ITERATION PROCESSES UNDER KANANN-SUZUKI-(C) CONDITION

1.
Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
3.
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), Spain

Author Bio: Email: bashirnawaz.482@gmail.com(B. Nawaz); Email: kifayatmath@yahoo.com(K. Ullah); Email: manuel.delasen@ehu.eus(M. De la Sen)
Corresponding author: Email: h.abdelwareth@qu.edu.sa(H. A. Hammad)
Fund Project: This work was supported in part by the Basque Government under Grant IT1555-22

Abstract

Abstract

In this paper, we study generalized ($C$)-conditions, specifically the Kannan-Suzuki-($C$) condition (abbreviated as the (KSC)-condition). We employ the M-iteration process to investigate the convergence behavior of mappings satisfying the KSC-condition and demonstrate that this approach offers improved convergence speed and computational efficiency compared to other well-known iteration schemes in the literature. To illustrate the advantages of the M-iteration process, we present new numerical examples that highlight its effectiveness. Additionally, we validate our theoretical findings by applying the method to fractional delay differential equations, showcasing its applicability in solving complex mathematical models. Furthermore, we compare the polynomiographs generated by the M-iteration process with those produced by other well-known iteration methods, demonstrating superior visualization properties and computational performance. These results establish the M-iteration process as a powerful tool for studying generalized contraction conditions.
- M-iteration /
- (KSC)-condition /
- fixed point /
- polynomiography /
- convergence /
- numerical method /
- iterative method
MSC: 47H09, 47H10

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References

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