Keywords:-
Keywords:
fixed point; digital image; digital metric space; contraction condition. 2020 Mathematical Sciences Classification: Primary: 54H25; Secondary: 47H10.
Article Content:-
Abstract
This study presents a fixed-point theorem in digital metric spaces under a hybrid contraction condition that combines standard distance terms with a nonlinear component involving square-root and minimum functions of distances. The proposed result generalizes classical contraction theorems, including those of Banach and Kannan offering a more flexible framework for fixed-point theory in discrete settings.
References:-
References
1. Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3(1), 133–181.
2. Boxer, L. (1990). Digitally continuous functions. Pattern Recognition Letters, 11(8), 363–367.
3. Chatterjea, S. K. (1972). Fixed point theorems. C.R. Acad. Bulgare Sci., 25(5), 727–730.
4. Ege, Ö., & Karaca, İ. (2015). Banach fixed point theorem for digital images. Journal of Nonlinear Science and Applications, 8(3), 237–245.
5. Han, S. E. (2006). Connected sum of digital closed surfaces. Information Sciences, 176(4), 332–348.
6. Kannan, R. (1968). Some results on fixed points. Bulletin of the Calcutta Mathematical Society, 60(1), 71–76.
7. Park, C., Ege, Ö., Kumar, S., Jain, D., & Lee, J. R. (2019). Fixed point theorems for various contraction conditions in digital metric spaces. Journal of Computational Analysis and Applications, 26(8), 1451–1458.
8. Reich, S. (1971). Some remarks concerning contraction mappings. Canadian Mathematical Bulletin, 14(1), 121–124.
9. Rosenfeld, A. (1979). Digital topology. American Mathematical Monthly, 86(1), 76–87
2. Boxer, L. (1990). Digitally continuous functions. Pattern Recognition Letters, 11(8), 363–367.
3. Chatterjea, S. K. (1972). Fixed point theorems. C.R. Acad. Bulgare Sci., 25(5), 727–730.
4. Ege, Ö., & Karaca, İ. (2015). Banach fixed point theorem for digital images. Journal of Nonlinear Science and Applications, 8(3), 237–245.
5. Han, S. E. (2006). Connected sum of digital closed surfaces. Information Sciences, 176(4), 332–348.
6. Kannan, R. (1968). Some results on fixed points. Bulletin of the Calcutta Mathematical Society, 60(1), 71–76.
7. Park, C., Ege, Ö., Kumar, S., Jain, D., & Lee, J. R. (2019). Fixed point theorems for various contraction conditions in digital metric spaces. Journal of Computational Analysis and Applications, 26(8), 1451–1458.
8. Reich, S. (1971). Some remarks concerning contraction mappings. Canadian Mathematical Bulletin, 14(1), 121–124.
9. Rosenfeld, A. (1979). Digital topology. American Mathematical Monthly, 86(1), 76–87
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Saluja, A., & Jhade, J. (2025). Fixed-Point Theorem for Nonlinear Contractions in Digital Metric Spaces. International Journal Of Mathematics And Computer Research, 13(11), 5854-5856. https://doi.org/10.47191/ijmcr/v13i11.02