Approximating Fixed Points of Implicit Almost Contractions FULL TEXT

Year 2012, Volume: 41 Issue: 1, 93 - 102, 01.01.2012

Vasile Berinde

Keywords

-

References

• Abbas, M. and Ilic, D. Common fixed points of generalized almost nonexpansive mappings, Filomat 24 (3), 11–18, 2010.
• 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.
• 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.
• 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.
• 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.
• 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.
• Berinde, V. On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19 (1), 7–22, 2003.
• Berinde, V. Approximating fixed points of weak ϕ-contractions, Fixed Point Theory 4 (2), –142, 2003.
• Berinde, V. Approximation fixed points of weak contractions using the Picard iteration, Nonlinear Analysis Forum, 9 (1), 43–53, 2004.
• Berinde, V. Error estimates for approximating fixed points of quasi contractions, General Math. 13 (2), 23ˆu-34, 2005.
• Berinde, V. Iterative Approximation of Fixed Points (Springer, Berlin, Heidelberg, New York, 2007).
• Berinde, V. General constructive fixed point theorems for ´Ciri´c-type almost contractions in metric spaces, Carpathian J. Math. 24 (2), 10–19, 2008.
• Berinde, V. Some remarks on a fixed point theorem for ´Ciri´c-type almost contractions, Carpathian J. Math. 25 (2), 157–162, 2009.
• Berinde, V. Approximating common fixed points of noncommuting almost contractions in metric spaces, Fixed Point Theory 11 (2), 179–188, 2010.
• Berinde, V. Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun. 15 (1), 229–241, 2010.
• Berinde, V. Stability of Picard iteration for contractive mappings satisfying an implicit relation, Carpathian J. Math. 27 (1), 13–23, 2011.
• Chatterjea, S. K. Fixed-point theorems, C. R. Acad. Bulgare Sci. 25, 727–730, 1972.
• 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.
• Kannan, R. Some results on fixed points, Bull. Calcutta Math. Soc. 10, 71–76, 1968.
• P˘acurar, M. Sequences of almost contractions and fixed points, Carpathian J. Math. 24 (2), –109, 2008.
• 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.
• Popa, V. Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bac˘au 7, 127–133, 1997.
• Popa, V. Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math. 32, 157–163, 1999.
• Popa, V. A general fixed point theorem for weakly compatible mappings in compact metric spaces, Turkish J. Math.25 (4), 465–474, 2001.
• 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.
• Popa, V. A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19, 45–51, 2005.
• 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.
• Popa, V. and Mocanu, M. Altering distance and common fixed points under implicit rela- tions, Hacet. J. Math. Stat. 38 (3), 329–337, 2009.
• Reich, S. Fixed points of contractive functions, Boll. Un. Mat. Ital. (4) 5, 26–42, 1972.
• Rhoades, B. E. A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226, 257–290, 1977.
• Rhoades, B. E. Contractive definitions revisited, Contemporary Mathematics 21 189–205, Rhoades, B. E. Contractive definitions and continuity, Contemporary Mathematics 72, 233– , 1988.
• 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)
• 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.
• 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.
• Walter, W. Remarks on a paper by F. Browder about contraction, Nonlinear Anal. TMA 5, –25, 1981.
• Zamfirescu, T. Fix point theorems in metric spaces, Arch. Math. (Basel) 23, 292–298, 1972.