Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

UNIQUE POINT OF COINCIDENCE FOR TWO MAPPINGS WITH 𝜑- OR 𝜓-𝜙-CONTRACTIVE CONDITIONS ON 2-METRIC SPACES

  • Xu, Ming-Xing (Department of Mathematics Yanbian University) ;
  • Huang, Xin (Department of Mathematics Yanbian University) ;
  • Piao, Yong-Jie (Department of Mathematics Yanbian University)
  • Received : 2016.01.11
  • Accepted : 2016.07.15
  • Published : 2016.08.15
Download PDF
⟨ Previous Next ⟩

Abstract

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

Keywords

References

  1. N. V. Dung, N. T. Hieu, N. T. Thanh Ly, and V. D. Thinh, Remarks on the fixed point problem of 2-metric spaces, Fixed Point Theory and Applications 2013: 167. Doi:10.1186/1687-1812-2013-167.
  2. N. V. Dung and V. T. L. Hang, Fixed point theorems for weak C-contractions in partially ordered 2-metric spaces, Fixed Point Theory and Applications 2013, 161. Doi:10.1186/1687-1812- 2013-161.
  3. B. K. Lahiri, Pratulananda Das and Lakshmi Kanta Dey, Cantor's theorem in 2-metric spaces and its applications to fixed point theorems, Taiwanese J. Math. 15 (2011), no. 1, 337-352. https://doi.org/10.11650/twjm/1500406178
  4. T. Phaneendra and K. K. Swamy, A unique common fixed point of a pare of self-maps on a 2-metric space, Mathematica Aeterna. 3 (2013), no. 4, 271-277.
  5. Y. J. Piao, Uniqueness of common fixed points for a family of maps with ${\phi}$j -quasi-contractive type in 2-metric space, Acta Mathematica Scientia 32 (2012), no. 6, 1079-1085.(In Chinese)
  6. Y. J. Piao, Uniqueness of common fixed point for a family of mappings with ${\phi}$-contractive condition in 2-metric space, Apllied Mathematics 3 (2012), 73-77.
  7. Y. J. Piao, New unique common fixed point theorems for a infinite family of mappings with ${\phi}$-${\psi}$-${\varphi}$-contractive conditions on 2-metric spaces, Advances in Fixed Point Theory 5 (2015), no. 4, 420-432.
  8. Y. J. Piao, Fixed point theorems for contractive and expansive mappings of Geraghty type on 2-metric spaces, Advances in Fixed Point Theory 6 (2016), no. 2, 123-135.
  9. S. L. Singh, Some contractive type principles on 2-metric spaces and applications, Mathematics Seminar Notes(Kobe University) 7 (1979), no. 1, 1-11.
  10. S. L. Singh, S. N. Sishira, and S. Stofile, Suzuki contraction theorem on a 2-metric space, J. Adv. Math. Stud. 5 (2012), no. 1, 71-76.
  11. H. S. Yang and D. S. Xiong, A common fixed point theorem on p-metric spaces, Journal of Yunnan Normal University(Science Edition) 21 (2001), no. 1, 9-12.
  12. D. Zhang and F. Gu, The common fixed point theorems for a class of ${\Phi}$-contraction conditions mappings in 2-metric spaces, Journal of Jiangxi Normal University(Natural Science) 35 (2011), no. 6, 595-600.(In Chinese)