Exploring the Rectangular Inequality in Bicomplex Valued Metric Spaces
Resumen
In this paper, we present a new space that extends the concept of bicomplex valued metric
spaces. We used rectangular inequality instead of triangular inequality. As a result, we have obtained some
new results regarding the complete bicomplex valued rectangular metric spaces. We employed the well-known
Banach contraction to investigate fixed points in bicomplex valued rectangular metric spaces. Moreover, we
give enough parameters so that two contractive mappings in bicomplex valued rectangular metric spaces have
a common fixed point. We also present several non-trivial cases to support the accuracy of our established
findings
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Citas
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spaces, Internat. J. Pure App. Math., (2011), 73(2), 159-164.
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Debrecen, (2000), 57(1-2), 31-37.
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mappings in bicomplex valued metric spaces, Honam Mathematical J., (2017), 39(1), 115-126.
14. F. Colombo, I. Sabadini D.C. Struppa, A. Vajiac, and M. Vajiac, Singularities of functions of one and several bicomplex
variables, Ark. Math., (2010), 49, 277-294.
15. B. S. Choudhury, N. Metiya, and V. Konar, Fixed point results for rational type contraction in partially ordered
complex valued metric spaces, Bulletin Internat. Math. Virtual Institute, (2015), 5, 73-80.
16. S. K. Datta, R. Sarkar, N. Biswas, and J. Saha, Common fixed point theorems for three self mappings in bicomplex
valued metric spaces. South East Asian J. Math. Math. Sci., (2021), 17(1), 297-308.
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Publishing, (2020).
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19. I.H. Jebril, S.K. Datta, R. Sarkar, and N. Biswas, Common fixed point theorems under rational contractions for a pair
of mappings in bicomplex valued metric spaces, J. Interdisciplinary Math., (2019), 22(7), 1071-1082.
20. M. E. Luna-Elizarraras, M. Shapiro, D.C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions,
Cubo., (2012), 14(2), 61-80.
21. G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, (1991).
22. A. C. M. Ran, and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix
equations, Proc. Amer. Math. Soc., (2003), 132, 1435-1443.
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Anal. Model. Control, (2016), 21(5), 614-634.
24. F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computer and
Mathematics with Applications, (2012),64(6), 1866-1874.
25. C. Segre, Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici, Math. Ann., (1892), 40, 413-467.
26. N. Spampinato, Singularities of functions of one and several bicomplex variables, Reale Accad. Naz. Lincei., (1935),
22(6), 38-43.
27. N. Spampinato, On the representation of totally differentiable functions of a bicomplex variable, Ann. Mat. Pura Appl,
(1936), 14(4), 305-325
45-48.
2. A. Azam, M. Arshad, and I. Beg, Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete
Math., (2009), 3(2), 236-241.
3. A. Azam, B. Fisher, and M. Khan, Common fixed point theorems in complex valued metric spaces, Number. Funct.
Anal. Optim., (2011), 32(3), 243-253.
4. J. Ahmad, A. Azam, and S. Saejung, Common fixed point results for contractive mappings in complex valued metric
spaces, Fixed Point Theory Appl., (2014), 1-11.
5. M. Arshad, J. Ahmad, and E. Karapinar, Some common fixed point results in rectangular metric spaces, Int. J.
Anal.,(2013), 1, 1-7.
6. S. Banach, Sur les operations dans les ensembles abs traits et leur application aux equations integrales, Fund. Math.,
(1922), 3, 133-181.
7. I. Beg, A. Azam, and M. Arshad, Common fixed points for maps on topological vector space valued cone metric spaces,
Internat. J. Math. & Math. Sci., (2009), 560264-1.
8. I. Beg, and A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric
spaces, Nonlinear Analysis: Theory, Methods and Applications, (2009), 71(9), 3699-3704.
9. K. Bhattacharjee, R. Das, B.C. Tripathy, & B. Hazarika, Contraction principle in bicomplex valued G-metric spaces
and its application in the system of linear equations, Boletim da Sociedade Paranaense de Matem ́atica, (2025), 43, 1-13.
https://doi.org/10.5269/bspm.76188
10. K. Bhattacharjee, R. Das, & B. C. Tripathy, Contraction principle in bicomplex valued multiplicative metric spaces,
Boletim da Sociedade Paranaense de Matem ́atica, (2026), 44, 1-10. https://doi.org/10.5269/bspm.77570
11. S. Bhatt, S. Chaukiyal, and R. C. Dimri, Fixed point of mapping satisfying rational inequality in complex valued metric
spaces, Internat. J. Pure App. Math., (2011), 73(2), 159-164.
12. A. Branciari,A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math.
Debrecen, (2000), 57(1-2), 31-37.
13. J. Choi, S. K. Datta, T. Biswas, and N. Islam, Some fixed point theorems in connection with two weakly compatible
mappings in bicomplex valued metric spaces, Honam Mathematical J., (2017), 39(1), 115-126.
14. F. Colombo, I. Sabadini D.C. Struppa, A. Vajiac, and M. Vajiac, Singularities of functions of one and several bicomplex
variables, Ark. Math., (2010), 49, 277-294.
15. B. S. Choudhury, N. Metiya, and V. Konar, Fixed point results for rational type contraction in partially ordered
complex valued metric spaces, Bulletin Internat. Math. Virtual Institute, (2015), 5, 73-80.
16. S. K. Datta, R. Sarkar, N. Biswas, and J. Saha, Common fixed point theorems for three self mappings in bicomplex
valued metric spaces. South East Asian J. Math. Math. Sci., (2021), 17(1), 297-308.
17. S. K. Datta, and R. Sarkar, Some new dimensional approach in bicomplex valued metric spaces, Lap Lambert Academic
Publishing, (2020).
18. G. Dragoni, Scorza., Sulle funzioni olomorfe di una variabile bicomplessa, Reale Accad. d’Italia, Mem. Classe Sci. Nat.
Fis. Mat., (1934), 5, 597-665.
19. I.H. Jebril, S.K. Datta, R. Sarkar, and N. Biswas, Common fixed point theorems under rational contractions for a pair
of mappings in bicomplex valued metric spaces, J. Interdisciplinary Math., (2019), 22(7), 1071-1082.
20. M. E. Luna-Elizarraras, M. Shapiro, D.C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions,
Cubo., (2012), 14(2), 61-80.
21. G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, (1991).
22. A. C. M. Ran, and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix
equations, Proc. Amer. Math. Soc., (2003), 132, 1435-1443.
23. J. R. R. Roshan, V. Parvaneh, and Z. Kadelburg, New fixed point results in b-rectangular metric spaces, Nonlinear
Anal. Model. Control, (2016), 21(5), 614-634.
24. F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computer and
Mathematics with Applications, (2012),64(6), 1866-1874.
25. C. Segre, Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici, Math. Ann., (1892), 40, 413-467.
26. N. Spampinato, Singularities of functions of one and several bicomplex variables, Reale Accad. Naz. Lincei., (1935),
22(6), 38-43.
27. N. Spampinato, On the representation of totally differentiable functions of a bicomplex variable, Ann. Mat. Pura Appl,
(1936), 14(4), 305-325
Publicado
2026-04-10
Sección
Special Issue: Non-Linear Analysis and Applied Mathematics
Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
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