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American Journal of Applied Mathematics and Statistics. 2018, 6(4), 135-140
DOI: 10.12691/AJAMS-6-4-3
Original Research

Some Common Fixed Point Theorems for Two Pairs of Weak Compatible Mappings of Type (A) in Gb-metric Space

M. Koierng Meitei1, Yumnam Rohen2, and R. S. Verma3

1Department of Mathematics, Modern College, Imphal East, Manipur, India

2Department of Mathematics, National Institute of Technology Manipur, Langol, Imphal-795004, Manipur, India

3NIMS University, Rajasthan, India

Pub. Date: August 01, 2018
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Cite this paper

M. Koierng Meitei, Yumnam Rohen and R. S. Verma. Some Common Fixed Point Theorems for Two Pairs of Weak Compatible Mappings of Type (A) in Gb-metric Space. American Journal of Applied Mathematics and Statistics. 2018; 6(4):135-140. doi: 10.12691/AJAMS-6-4-3

Abstract

In this paper, we prove a common fixed point theorem for two pairs of weak compatible mappings of type (A) in Gb-metric space. Further our result is verified with the help of example.

Keywords

common fixed point, Gb-metric spaces, weak compatible mappings of type (A)

Copyright

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]  Aghajani A., Abbas M. and Roshan J. R., Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered Gb-metric Spaces, Filomat28:6 (2014), 1087-1101.
 
[2]  Mustafa Z, Sims B. A new approach to generalized metric spaces. J Nonlinear Convex Anal, 2006, 7: 289297.
 
[3]  I. A. Bakhtin, The contraction principle in quasimetric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk, 30(1989), 26-37.
 
[4]  Czerwik, S. Contraction mappings in b−metric spaces, Acta Math. Inf. Univ. Ostraviensis.1, (1993), 5-11.
 
[5]  Czerwik, S. Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Sem. Mat. Fis. Univ. Modena, 46(2), (1998), 263-276.
 
[6]  Z. Mustafa, J.R. Roshan and V. Parvaneh, Coupled coincidence point results for (ψ, φ)-weakly contractive mappings in partially ordered Gb-metric spaces, Fixed Point Theory Appl., 2013:206 (2013).
 
[7]  Z. Mustafa, J. R. Roshan and V. Parvaneh, Existence of a tripled coincidence point in ordered Gb-metric spaces and applications to a system of integral equations, Journal of Inequalities and Applications 2013, 2013:453.
 
[8]  Shaban Sedghi, Nabi Shobkolaei, Jamal Rezaei Roshan and Wasfi Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Matematiki Vesnik, 66, 2 (2014), 190-201 June 2014.
 
[9]  Bulbul Khomdram, Yumnam Rohen and Thokchom Chhatrajit Singh, Coupled fixed point theorems in Gb-metric space satisfying some rational contractive conditions, SpringerPlus (2016), 5:1261.
 
[10]  Bulbul Khomdram and Yumnam Rohen, Quadrupled common fixed point theorems in Gb-metric spaces, IJPAM, 109(2), (2016), 279-293.
 
[11]  G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (4) (1986), 771-779.
 
[12]  Jungck, G., Murthy, P. P. and Cho, Y. J., Compatible mappings of type (A) and common fixed points, Math. Japonica, 38, (1993), 381-390.
 
[13]  Pathak, H. K., Kang, S. M. and Baek, J. H., Weak compatible mappings of type (A) and common fixed point in Menger spaces, Comm. Korean Math. Soc., 10 (1), (1995), 67-83.
 
[14]  Yumnam Rohen and Bidya Devi, Relationship between various types of compatible mappings, IJMSEA, 4(I) (2010), 67-82.
 
[15]  Yumnam Rohen, Fixed point theorems of compatible mappings of type(R) in metric spaces, Int. J. Open Problems Compt. Math., 3(5), (2010) 138-143.
 
[16]  L. Dwijendra and Yumnam Rohen, Common fixed point theorems of compatible mappings of type (A) in fuzzy metric spaces, IJMSEA, 5(VI) (2011), 307-316.
 
[17]  M. Koireng and Yumnam Rohen, Common fixed point theorems of compatible mappings of type (P) in fuzzy metric spaces, Int. J. of Math. Anal., 6(4), (2012), 181-188.
 
[18]  L. Ibeni and Yumnam Rohen, Related fixed point theorems for three set-valued mappings on three uniform spaces, Int. J. of Math. Anal., 6(9), (2012), 415-427
 
[19]  M. Krishnanado, Yumnam Rohen and L. Shambhu, Common fixed point theorems of compatible mappings of type(R), IJMSEA, 6(I) (2012), 355-361.
 
[20]  Yumnam Rohen, Th. Indubala, O. Budhichandra and Leenthoi N., Common fixed point theorem for compatible mappings of type (A), IJMSEA, 6(II) (2012), 323-333.
 
[21]  M. Krishnanando, Yumnam Rohen, O. Budhichandra and Mairembam Bina, Weak compatible and compatible mappings of type (R) in cone metric space, IJMSEA, 6(II) (2012), 161-170.
 
[22]  M. Koireng Meitei and Yumnam Rohen, Some fixed point theorems for compatible mappings in uniform space, IJMSEA, 6(IV) (2012), 107-115.
 
[23]  M. Koireng Meitei Leenthoi N. and Yumnam Rohen, Common fixed points of compatible mappings of type (R), General Mathematics Notes, 10(1) (2012), 58-62.
 
[24]  M. Popeshwar Singh and Yumnam Rohen, Common fixed points of compatible mappings, Journal of Scientific Research, 4(3) (2012), 603-608.
 
[25]  L. Ibeni Devi and Yumnam Rohen, Compatible mappings of type (A-1) and type (A-2) in cone metric space, The Journal of Mathematics and Computer Sciences 2(6), (2012), 1612-1621.
 
[26]  Yumnam Rohen and M. Ranjit Singh, Compatible mappings in cone metric space, for the book “Weakly commuting mappings after thirty years in metric fixed point theory” edited by S. Sessa, 2012 47-54.
 
[27]  Shahidur Rahman, Yumnam Rohen and M. Popeshwar Singh, Generalised common fixed point theorems of A-compatible and S-compatible mappings, American J. of Applied Mathematics and Statistics, 1(2), (2013), 27-29.
 
[28]  L. Ibeni Devi and Yumnam Rohen, Remarks on common fixed point theorems of Rajesh et. al., IJMSEA, 7(VI) (2013) 97-109.
 
[29]  L. Bishwakumar and Yumnam Rohen, Common fixed point theorem for six self-maps in a cone metric space through semi compatibility and weak compatibility, IJMSEA, 7(VI) (2013) 121-133.
 
[30]  Yumnam Rohen and L. Premila Devi, Some fixed point theorems of semicompatible mappings, Journal of International Academy of Physical Sciences, 18(2) (2014) 125-129.
 
[31]  Thokchom Chhatrajit and Yumnam Rohen, A comparative study of relationship among various types of spaces, International Journal of Applied Mathematics, 28(1) (2015), 29-36.
 
[32]  Yumnam Rohen and L. Premila Devi, Some fixed point theorems of semi compatible and occasionally weakly compatible mappings in menger space, American Journal of Applied Mathematics and Statistics, 3(1) (2015), 29-33.
 
[33]  Laishram Shanjit, Yumnam Rohen and P. P. Murthy, Some fixed point theorems of R-weakly commuting mappings in multiplicative metric spaces, Gazi University Journal of Science, 29(4) (2016) 855-867.