Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME FIXED POINT THEOREMS IN CONNECTION WITH TWO WEAKLY COMPATIBLE MAPPINGS IN BICOMPLEX VALUED METRIC SPACES

  • Received : 2016.12.12
  • Accepted : 2017.01.26
  • Published : 2017.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we aim to prove certain common fixed point theorems for a pair of weakly compatible mappings satisfying (CLRg) (or (E.A)) property in the bicomplex valued metric spaces. We also provide some examples which support the main results here.

Keywords

References

  1. A. Azam, F. Brain and M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim. 32 (3) (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046
  2. R. Agarwal, M. P. Goswami and R. P. Agarwal, Convolution theorem and applications of bicomplex Laplace transform, Adv. Math. Sci. Appl. 24(1) (2014), 113-127.
  3. R. Agarwal, M. P. Goswami and R. P. Agarwal, Tauberian theorem and applications of bicomplex Laplace-Stieltjes transform, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 22 (2015), 141-153.
  4. R. Agarwal, M. P. Goswami and R. P. Agarwal, Bicomplex version of Stieltjes transform and applications, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 21 (2014), 229-246.
  5. A. Banerjee, S. K. Datta and A. Hoque, Inverse Laplace transform for bicomplex variables, Math. Inverse Probl. 1(1) (2014), 8-14.
  6. K. S. Charak, R. Kumar and D. Rochon, In nite dimensional bicomplex spectral decomposition theorem, Adv. Appl. Cli ord Algebras 23 (2013), 593-605. https://doi.org/10.1007/s00006-013-0385-5
  7. J. Choi, S. K. Datta, T. Biswas and Md N. Islam, Certain common xed point theorems for two weakly compatible mappings in bicomplex valued metric spaces, submiited for publication (2016).
  8. M. E. Luna-Elizarraras, M. Shapiro, D. C. Struppa and A. Vajiac, Bicomplex numbers and their elementary functions, Cubo 14(2) (2012), 61-80. https://doi.org/10.4067/S0719-06462012000200004
  9. R. G. Lavoie, L. Marchildon and D. Rochon, In nite-dimensional bicomplex Hilbert spaces, Ann. Funct. Anal. 1(2) (2010), 75-91. https://doi.org/10.15352/afa/1399900590
  10. R. G. Lavoie, L. Marchildon and D. Rochon, Hilbert space of the bicomplex quantum harmonic oscillator, AIP Conf. Proc. 1327 (2011), 148-157.
  11. R. G. Lavoie, L. Marchildon and D. Rochon, Finite-dimensional bicomplex Hilbert spaces, Adv. Appl. Cli ord Algebras 21(3) (2011), 561-581. https://doi.org/10.1007/s00006-010-0274-0
  12. A. Kumar and P. Kumar, Bicomplex version of Laplace transform, Internat. J. Engrg. Tech. 3(3) (2011), 225-232.
  13. G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, 1991.
  14. D. Rochon and M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, An. Univ. Oradea Fasc. Mat. 11 (2004), 71-110.
  15. C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann. 40 (1892), 413-467. https://doi.org/10.1007/BF01443559
  16. N. Spampinato, Estensione nel campo bicomplesso di due teoremi, del Levi- Civita e del Severi, per le funzioni olomorfe di due variablili bicomplesse I, II, Reale Accad. Naz. Lincei 22(6) (1935), 38-43, 96-102.
  17. N. Spampinato, Sulla Rappresentazione delle funzioni do variabile bicomplessa totalmente derivabili, Ann. Mat. Pura Appl. 14(4) (1936), 305-325.
  18. G. Scorza Dragoni, Sulle funzioni olomorfe di una variabile bicomplessa, Reale Accad. d'Italia, Mem. Classe Sci. Nat. Fis. Mat. 5 (1934), 597-665.
  19. W. Sintunavarat, P. Kumam, Common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. 2011 (2011):14, Article ID 637958.