Common Fixed Point Results for Compatible Mappings of Type (C)

  • Mumtaz Ali Department of Mathematics, Federal Government College, Mardan (KPK), Pakistan
  • Muhammad Arshad Department of Mathematics, International Islamic University, H-10, Islamabad-44000, Pakistan
Keywords: compatible mappings, compatible mappings of type (C), common fixed points, complete metric space

Abstract

The aim of this paper is to study and generalize common fixed point theorems for four self-mappings compatible of type (C) in the settings of complete metric spaces. The main idea is the extensions and generalizations of some fixed point theorems related to compatible mappings.

References

Abbas, M., & Jungck, G. (2008). Common fixed point results for noncommuting mappings without continuity in cone metric spaces. Journal of Mathematical Analysis and Applications, 341, 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070

Akkouchi, M. (2011). Common fixed points for weakly compatible maps satisfying implicit relations without continuity. Demonstratio Mathematica, 44(1), 151-158. https://doi.org/10.1515/dema-2013-0289

Aamri, M., & El Moutawakil, D. (2002). Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications, 270, 181-188. https://doi.org/10.1016/s0022-247x(02)00059-8

Anil, K. D., & Urmila, M. (2014). Coincident points and common fixed point results for three mappings in cone metric spaces, I. International Journal of Nonlinear Analysis and Applications, 2, 104-110.

Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133-181. https://doi.org/10.4064/fm-3-1-133-181

Chugh, R., & Kumar, S. (2011). Common fixed points for weakly compatible maps. Proc. Indian Acad. (Math. Sci.), 111(2), 241-247. https://doi.org/10.1007/bf02829594

Das, K. M., & Naik, K. V. (1979). Common fixed point theorems for commuting maps on a metric space. Proceedings of the American Mathematical Society, 77, 369-373. https://doi.org/10.2307/2042188

Fisher, B. (1983). Common fixed points of four mappings. Bulletin of the Institute of Mathematics, Academia Sinica, 11, 103-113.

Fisher, B. (1976). Fixed point and constant mappings on metric spaces. Atti Accad, Naz., Lincci Rend. Ci. Sci. Mat. Natur., 61, 329-332. https://doi.org/10.1472/doiserialissuework2.0

Djoudi, A. (2003). A common fixed point theorem for compatible mappings of type (B) in complete metric spaces. Demonstratio Mathematica, 36(2), 463-470. https://doi.org/10.1515/dema-2003-0220

Hardy, G. E., & Rogers, T. D. (1973). A generalization of a fixed point theorem of Reich. Canadian Mathematical Bulletin, 16(2), 201-206. https://doi.org/10.4153/cmb-1973-036-0

Jungck, G. (1976). Commuting mappings and fixed points. The American Mathematical Monthly, 83, 261-263. https://doi.org/10.1080/00029890.1976.11994093

Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9, 771-779. https://doi.org/10.1155/s0161171286000935

Jungck, G., Murthy, P. P., & Cho, Y. J. (1993). Compatible mappings of type (A) and common fixed points. Mathematica Japonica, 36, 381-390.

Jungck, G., & Rhoades, B. E. (1998). Fixed points for set-valued functions without continuity. Indian Journal of Pure and Applied Mathematics, 29(3), 227-238.

Kannan, R. (1968). Some results on fixed points. Bulletin of the Calcutta Mathematical Society, 10, 71-76.

Mukerjee, R. N. (1981). Common fixed points of some nonlinear mappings. Indian Journal of Pure and Applied Mathematics, 12(8), 930-933.

Pant, K. P. (1998). Common fixed points of four mappings. Bulletin of the Calcutta Mathematical Society, 9, 281-286.

Pathak, H. K., Chang, S. S., & Cho, Y. J. (1994). Fixed point theorems for compatible mappings of type (P). Indian Journal of Mathematics, 36(2), 151-166.

Pathak, H. K., Cho, Y. J., Kang, S. M., & Lee, B. S. (1995). Fixed point theorems for compatible mappings of type (P) and applications to dynamic programming. Le Matematiche, 1, 15-33.

Pathak, H. K., Chen, Y. J., Khan, M. S., & Madhuria, B. (1998). Compatible mappings of type (C) and common fixed point theorems of Gregus type. Demonstratio Mathematica, 31(3), 499-518.

Pathak, H. K., & Khan, M. S. (1997). A comparison of various types of compatible maps and common fixed points. Indian Journal of Pure and Applied Mathematics, 28, 477-485.

Popa, V. (2001). Some fixed point theorems for weakly compatible mappings. Radovi Matematički, 10, 219-252.

Rhoades, R. E. (2001). Some theorems on weakly contractive maps. Nonlinear Analysis, 47, 2683-2693. https://doi.org/10.1016/s0362-546x(01)00388-1

Rohen, Y., Indubala, Th., Budhichandra, O., & Leenthoi, N. (2012). Common fixed point theorems for compatible mappings of type (A). International Journal of Mathematics, Science, Engineering and Advancement, 6(II), 323-333.

Rohen, Y., & Singh, M. R. (2008). Common fixed points of compatible mappings of type (R) in complete metric spaces. International Journal of Mathematics, Science, Engineering and Advancement, 2(IV), 295-303.

Sharma, P. L., & Sahu, M. K. (1991). A unique fixed point theorem in complete metric space. Acta Ciencia Indica. Mathematics, 17(4), 685-688.

Sessa, S. (1982). On a weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique (Beograd), 32, 149-153.

Singh, S. L. (1977). On common fixed points of commuting mappings. Math. Seminar Notes Kobe Univ., 5, 131-134.

Sedghi, S., & Shobe, N. (2007). Common fixed point theorems for four mappings in complete metric spaces. Bulletin of the Iranian Mathematical Society, 33(2), 37-47.

Tas, K., Telci, M., & Fisher, B. (1996). Common fixed point theorems for compatible mappings. International Journal of Mathematics and Mathematical Sciences, 19(3), 451-456. https://doi.org/10.1155/s0161171296000646

Published
2023-09-21
How to Cite
Ali, M., & Arshad, M. (2023). Common Fixed Point Results for Compatible Mappings of Type (C). Earthline Journal of Mathematical Sciences, 13(2), 527-542. https://doi.org/10.34198/ejms.13223.527542
Section
Articles