Approximating Fixed Points of Implicit Almost Contractions FULL TEXT

Abstract

-

Keywords

• -

References

1. Abbas, M. and Ilic, D. Common fixed points of generalized almost nonexpansive mappings, Filomat 24 (3), 11–18, 2010.
2. Abbas, M., Vetro, P. and Khan, S. H. On fixed points of Berinde’s contractive mappings in cone metric spaces, Carpathian J. Math. 26 (2), 121–133, 2010.
3. Ali, J. and Imdad, M. Unifying a multitude of common fixed point theorems employing an implicit relation, Commun. Korean Math. Soc. 24 (1), 41–55, 2009.
4. Aliouche, A. and Djoudi, A. Common fixed point theorems for mappings satisfying an im- plicit relation without decreasing assumption, Hacet. J. Math. Stat. 36 (1), 11–18, 2007.
5. Aliouche, A. and Popa, V. General common fixed point theorems for occasionally weakly compatible hybrid mappings and applications, Novi Sad J. Math. 39 (1), 89–109, 2009.
6. Babu, G. V. R., Sandhy, M. L. and Kameshwari, M. V. R. A note on a fixed point theorem of Berinde on weak contractions, Carpathian J. Math. 24 (1), 8–12, 2008.
7. Berinde, V. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19 (1), 7–22, 2003.
8. Berinde, V. Approximating fixed points of weak ϕ-contractions, Fixed Point Theory 4 (2), –142, 2003.

9. Berinde, V. Approximation fixed points of weak contractions using the Picard iteration, Nonlinear Analysis Forum, 9 (1), 43–53, 2004.
10. Berinde, V. Error estimates for approximating fixed points of quasi contractions, General Math. 13 (2), 23ˆu-34, 2005.
11. Berinde, V. Iterative Approximation of Fixed Points (Springer, Berlin, Heidelberg, New York, 2007).
12. Berinde, V. General constructive fixed point theorems for ´Ciri´c-type almost contractions in metric spaces, Carpathian J. Math. 24 (2), 10–19, 2008.
13. Berinde, V. Some remarks on a fixed point theorem for ´Ciri´c-type almost contractions, Carpathian J. Math. 25 (2), 157–162, 2009.
14. Berinde, V. Approximating common fixed points of noncommuting almost contractions in metric spaces, Fixed Point Theory 11 (2), 179–188, 2010.
15. Berinde, V. Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun. 15 (1), 229–241, 2010.
16. Berinde, V. Stability of Picard iteration for contractive mappings satisfying an implicit relation, Carpathian J. Math. 27 (1), 13–23, 2011.
17. Chatterjea, S. K. Fixed-point theorems, C. R. Acad. Bulgare Sci. 25, 727–730, 1972.
18. Di Bari, C. and Vetro, P. Weakly φ-pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo (2) 58 (1), 125–132, 2009.
19. Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc. 10, 71–76, 1968.
20. P˘acurar, M. Sequences of almost contractions and fixed points, Carpathian J. Math. 24 (2), –109, 2008.
21. P˘acurar, M. Iterative Methods for Fixed Point Approximation (Risoprint, Cluj-Napoca, ). P˘acurar, M. A multi-step iterative method for approximating fixed points of Preˇsi´c-Kannan operators, Acta Math. Univ. Comenian. (N. S.) 79 (1), 77–88, 2010.
22. Popa, V. Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bac˘au 7, 127–133, 1997.
23. Popa, V. Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32, 157–163, 1999.
24. Popa, V. A general fixed point theorem for weakly compatible mappings in compact metric spaces, Turkish J. Math.25 (4), 465–474, 2001.
25. Popa, V. Fixed points for non-surjective expansion mappings satisfying an implicit relation, Bul. S¸tiint¸. Univ. Baia Mare Ser. B Fasc. Mat.-Inform 18 (1), 105–108, 2002.
26. Popa, V. A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19, 45–51, 2005.
27. Popa, V., Imdad, M. and Ali, J. Using implicit relations to prove unified fixed point theorems in metric and 2-metric spaces, Bull. Malays. Math. Sci. Soc. (2) 33 (1), 105–120, 2010.
28. Popa, V. and Mocanu, M. Altering distance and common fixed points under implicit rela- tions, Hacet. J. Math. Stat. 38 (3), 329–337, 2009.
29. Reich, S. Fixed points of contractive functions, Boll. Un. Mat. Ital. (4) 5, 26–42, 1972.
30. Rhoades, B. E. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226, 257–290, 1977.
31. Rhoades, B. E. Contractive definitions revisited, Contemporary Mathematics 21 189–205, Rhoades, B. E. Contractive definitions and continuity, Contemporary Mathematics 72, 233– , 1988.
32. Rus, I. A. Generalized Contractions and Applications (Cluj University Press, Cluj-Napoca, ). Rus, I. A., Petru¸sel, A. and Petru¸sel, G. Fixed Point Theory (Cluj University Press, Cluj- Napoca, 2008)
33. Singh, M. R. and Singh, Y. M. On various types of compatible maps and common fixed point theorems for non-continuous maps, Hacet. J. Math. Stat. 40 (4), 503–513, 2011.
34. Vetro, P., Azam, A. and Arshad, M. Fixed point results in cone metric spaces for contrac- tions of Zamfirescu type, Indian J. Math. 52 (2), 251–261, 2010.
35. Walter, W. Remarks on a paper by F. Browder about contraction, Nonlinear Anal. TMA 5, –25, 1981.
36. Zamfirescu, T. Fix point theorems in metric spaces, Arch. Math. (Basel) 23, 292–298, 1972.