Matkowski’s fixed point theorem in Rm-b-metric spaces
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Abstract
In this paper, we aim to extend the fixed point theorem in metric spaces to Rm-b-metric spaces. By constructing iterated sequences and proving that they are Cauchy sequences, we have established and proven the Matkowski fixed point theorem in Rm-b-metric spaces. In addition, an example is presented to illustrate the obtained result.
Keywords
Contraction, fixed point, R^m-b-metric space
Article Details
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References
Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3(1), 133-181.
Bazine, S. (2022). Fixed point of four maps in generalized b-metric spaces. International Journal of Nonlinear Analysis and Applications, 13(1), 2723-2730. https://doi.org/10.22075/ijnaa.2021.24581.2776
Boriceanu, M. (2009). Fixed point theory on spaces with vector-valued b-metrics. Demonstratio Mathematica, 42(4), 825-836. https://doi.org/10.1515/dema-2009-0415
Boyd, D. W., & Wong, J. S. (1969). On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2), 458-464. https://doi.org/10.2307/2035677
Ćirić, L. B. (1974). A generalization of Banach’s contraction principle. Proceedings of the American Mathematical society, 45(2), 267-273. https://doi.org/10.1090/S0002-9939-1974-0356011-2
Coifman, R. R., & de Guzmán, M. (1970). Singular integrals and multipliers on homogeneous spaces. Rev. Un. Mat. Argentina, 25(137-143), 71.
Czerwik, S. (1993). Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis, 1(1), 5-11.
Kannan, R. (1969). Some results on fixed points—II. The American Mathematical Monthly, 76(4), 405-408.
Kirk, W., & Shahzad, N. (2014). Fixed point theory in distance spaces.
Kirk, W. A., & Sims, B. (2001). Handbook of metric fixed point theory, Kluwer Academic.
Matkowski, J. (1975). Integrable solutions of functional equations, Dissertationes Math., 127 (1975), 1-68.
Perov, A. I. (1964). On the Cauchy problem for a system of ordinary differential equations. Pviblizhen. Met. Reshen. Differ. Uvavn, 2(1964), 115-134.
Bazine, S. (2022). Fixed point of four maps in generalized b-metric spaces. International Journal of Nonlinear Analysis and Applications, 13(1), 2723-2730. https://doi.org/10.22075/ijnaa.2021.24581.2776
Boriceanu, M. (2009). Fixed point theory on spaces with vector-valued b-metrics. Demonstratio Mathematica, 42(4), 825-836. https://doi.org/10.1515/dema-2009-0415
Boyd, D. W., & Wong, J. S. (1969). On nonlinear contractions. Proceedings of the American Mathematical Society, 20(2), 458-464. https://doi.org/10.2307/2035677
Ćirić, L. B. (1974). A generalization of Banach’s contraction principle. Proceedings of the American Mathematical society, 45(2), 267-273. https://doi.org/10.1090/S0002-9939-1974-0356011-2
Coifman, R. R., & de Guzmán, M. (1970). Singular integrals and multipliers on homogeneous spaces. Rev. Un. Mat. Argentina, 25(137-143), 71.
Czerwik, S. (1993). Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis, 1(1), 5-11.
Kannan, R. (1969). Some results on fixed points—II. The American Mathematical Monthly, 76(4), 405-408.
Kirk, W., & Shahzad, N. (2014). Fixed point theory in distance spaces.
Kirk, W. A., & Sims, B. (2001). Handbook of metric fixed point theory, Kluwer Academic.
Matkowski, J. (1975). Integrable solutions of functional equations, Dissertationes Math., 127 (1975), 1-68.
Perov, A. I. (1964). On the Cauchy problem for a system of ordinary differential equations. Pviblizhen. Met. Reshen. Differ. Uvavn, 2(1964), 115-134.
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