## Abstract and Applied Analysis

### Common Fixed Points for Pairs of Mappings with Variable Contractive Parameters

#### Abstract

We establish some common fixed point results for a new class of pair of contraction mappings having functions as contractive parameters, and satisfying minimal noncommutative operators property.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 209234, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606982

Digital Object Identifier
doi:10.1155/2014/209234

Mathematical Reviews number (MathSciNet)
MR3178853

Zentralblatt MATH identifier
07021932

#### Citation

Morales, J. R.; Rojas, E. M.; Bisht, Ravindra K. Common Fixed Points for Pairs of Mappings with Variable Contractive Parameters. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 209234, 7 pages. doi:10.1155/2014/209234. https://projecteuclid.org/euclid.aaa/1412606982

#### References

• G. Jungck, “Commuting mappings and fixed points,” The American Mathematical Monthly, vol. 83, no. 4, pp. 261–263, 1976.
• M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bulletin of the Australian Mathematical Society, vol. 30, no. 1, pp. 1–9, 1984.
• G. Jungck, “Compatible mappings and common fixed points,” International Journal of Mathematics and Mathematical Sciences, vol. 9, no. 4, pp. 771–779, 1986.
• M. Aamri and D. El Moutawakil, “Some new common fixed point theorems under strict contractive conditions,” Journal of Mathematical Analysis and Applications, vol. 270, no. 1, pp. 181–188, 2002.
• W. Sintunavarat and P. Kumam, “Gregus type fixed points for a tangential multi-valued mappings satisfying contractive conditions of integral type,” Journal of Inequalities and Applications, vol. 2011, article 3, 2011.
• L. B. Ćirić, “On some maps with a nonunique fixed point,” Publications de l'Institut Mathématique, vol. 17(31), pp. 52–58, 1974.
• G. Jungck and B. E. Rhoades, “Fixed point theorems for occasionally weakly compatible mappings,” Fixed Point Theory, vol. 7, no. 2, pp. 287–296, 2006.
• M. A. Al-Thagafi and N. Shahzad, “Generalized $I$-nonexpansive selfmaps and invariant approximations,” Acta Mathematica Sinica, vol. 24, no. 5, pp. 867–876, 2008.
• G. V. R. Babu and P. D. Sailaja, “A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces,” Thai Journal of Mathematics, vol. 9, no. 1, pp. 1–10, 2011.
• Z. Liu, X. Li, S. Minkan, and S. Y. Cho, “Fixed point theorems for mappings satisfying contractive conditions of integral type and applications,” Fixed Point Theory and Applications, vol. 2011, article 64, 2011.
• R. P. Pant and R. K. Bisht, “Occasionally weakly compatible mappings and fixed points,” Bulletin of the Belgian Mathematical Society. Simon Stevin, vol. 19, no. 4, pp. 655–661, 2012.
• D. Delbosco, “Un'estensione di un teorema sul punto fisso di S. Reich,” Rendiconti del Seminario Matematico Università e Politecnico di Torino, vol. 35, pp. 233–238, 1976-1977.
• F. Skof, “Teoremi di punto fisso per applicazioni negli spazi metrici,” Atti della Accademia delle Scienze di Torino. Classe di Scienze Fisiche, Matematiche e Naturali, vol. 111, no. 3-4, pp. 323–329, 1977.
• P. N. Dutta and B. S. Choudhury, “A generalisation of contraction principle in metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 406368, 8 pages, 2008.
• P. N. Dutta, B. S. Choudhury, and K. Das, “Some fixed point results in Menger spaces using a control function,” Surveys in Mathematics and Its Applications, vol. 4, pp. 41–52, 2009.
• J. R. Morales and E. M. Rojas, “Some generalizations of Jungck's fixed point theorem,” International Journal of Mathematics and Mathematical Sciences, vol. 2012, Article ID 213876, 19 pages, 2012.
• J. R. Morales and E. Rojas, “Some fixed point theorems by altering distance functions,” Palestine Journal of Mathematics, vol. 1, no. 2, pp. 110–116, 2012.
• S. V. R. Naidu, “Some fixed point theorems in metric spaces by altering distances,” Czechoslovak Mathematical Journal, vol. 53, no. 1, pp. 205–212, 2003.
• H. K. Nashine, B. Samet, and J. K. Kim, “Fixed point results for contractions involving generalized altering distances in ordered metric spaces,” Fixed Point Theory and Applications, vol. 2011, article 5, 2011.
• K. P. R. Sastry and G. V. R. Babu, “Some fixed point theorems by altering distances between the points,” Indian Journal of Pure and Applied Mathematics, vol. 30, no. 6, pp. 641–647, 1999.
• J. Jachymski, “Equivalent conditions for generalized contractions on (ordered) metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 3, pp. 768–774, 2011.
• A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, pp. 531–536, 2002.
• A. Aliouche, “A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type,” Journal of Mathematical Analysis and Applications, vol. 322, no. 2, pp. 796–802, 2006.
• H. Aydi, “A common fixed point result by altering distances involving a contractive condition of integral type in partial metric spaces,” Demonstratio Mathematica, vol. 46, no. 2, pp. 383–394, 2013.
• Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet, and W. Shatanawi, “Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type,” Fixed Point Theory and Applications, vol. 2012, article 8, 2012.
• B. E. Rhoades, “Two fixed-point theorems for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 2003, no. 63, pp. 4007–4013, 2003.
• B. Samet and C. Vetro, “An integral version of Ćirić's fixed point theorem,” Mediterranean Journal of Mathematics, vol. 9, no. 1, pp. 225–238, 2012.
• J. Jachymski, “Remarks on contractive conditions of integral type,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 3-4, pp. 1073–1081, 2009.
• M. Abbas and M. A. Khan, “Common fixed point theorem of two mappings satisfying a generalized weak contractive condition,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 131068, 9 pages, 2009.
• V. Popa and M. Mocanu, “Altering distance and common fixed points under implicit relations,” Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 329–337, 2009. \endinput