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Hussain, N.; Kutbi, M. A.; Khaleghizadeh, S.; Salimi, P.

Discussions on recent results for \(\alpha\)-\(\psi\)-contractive mappings. (English) Zbl 1469.54117

Abstr. Appl. Anal. 2014, Article ID 456482, 13 p. (2014).
Summary: We establish certain fixed point results for \(\alpha - \eta\)-generalized convex contractions, \(\alpha - \eta\)-weakly Zamfirescu mappings, and \(\alpha - \eta\)-Ćirić strong almost contractions. As an application, we derive some Suzuki type fixed point theorems and certain new fixed point theorems in metric spaces endowed with a graph and a partial order. Moreover, we discuss some illustrative examples to highlight the realized improvements.

Cited in 13 Documents

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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[1] Espínola, R.; Kirk, W. A., Fixed point theorems in \(R\)-trees with applications to graph theory, Topology and its Applications, 153, 7, 1046-1055 (2006) · Zbl 1095.54012 · doi:10.1016/j.topol.2005.03.001
[2] Agarwal, R. P.; Hussain, N.; Taoudi, M.-A., Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstract and Applied Analysis, 2012 (2012) · Zbl 1252.47044
[3] Abbas, M.; Altun, I.; Romaguera, S., Common fixed points of Ćirić-type contractions on partial metric spaces, Publicationes Mathematicae Debrecen, 82, 2, 425-438 (2013) · Zbl 1299.54074 · doi:10.5486/PMD.2013.5342
[4] Ćirić, L. B., A generalization of Banach’s contraction principle, Proceedings of the American Mathematical Society, 45, 267-273 (1974) · Zbl 0291.54056
[5] Ćirić, L.; Hussain, N.; Cakić, N., Common fixed points for Ćirić type \(f\)-weak contraction with applications, Publicationes Mathematicae Debrecen, 76, 1-2, 31-49 (2010) · Zbl 1261.47071
[6] Ćirić, L.; Abbas, M.; Saadati, R.; Hussain, N., Common fixed points of almost generalized contractive mappings in ordered metric spaces, Applied Mathematics and Computation, 217, 12, 5784-5789 (2011) · Zbl 1206.54040 · doi:10.1016/j.amc.2010.12.060
[7] Geraghty, M. A., On contractive mappings, Proceedings of the American Mathematical Society, 40, 604-608 (1973) · Zbl 0245.54027 · doi:10.1090/S0002-9939-1973-0334176-5
[8] Gopal, M.; Imdad, M.; Vetro, C.; Hasan, M., Fixed point theory for cyclic weak \(\phi \)-contraction in fuzzy metric spaces, Journal Nonlinear Analysis and Application (2012)
[9] Hussain, N.; Karapınar, E.; Salimi, P.; Akbar, F., \( \alpha \)-admissible mappings and related fixed point theorems, Journal of Inequalities and Applications, 2013: article 114 (2013) · Zbl 1293.54023 · doi:10.1186/1029-242X-2013-114
[10] Hussain, N.; Khamsi, M. A., On asymptotic pointwise contractions in metric spaces, Nonlinear Analysis: Theory, Methods & Applications, 71, 10, 4423-4429 (2009) · Zbl 1176.54031 · doi:10.1016/j.na.2009.02.126
[11] Yao, J.-C.; Zeng, L.-C., Fixed point theorem for asymptotically regular semigroups in metric spaces with uniform normal structure, Journal of Nonlinear and Convex Analysis, 8, 1, 153-163 (2007) · Zbl 1121.47045
[12] Istrăţescu, V. I., Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters. I, Annali di Matematica Pura ed Applicata, 130, 4, 89-104 (1982) · Zbl 0477.54033 · doi:10.1007/BF01761490
[13] Miandaragh, M. A.; Postolache, M.; Rezapour, Sh., Approximate fixed points of generalized convex contractions, Fixed Point Theory and Applications, 2013, article 255 (2013) · Zbl 1289.54135
[14] Salimi, P.; Latif, A.; Hussain, N., Modified alpha-psi-contractive mappings with applications, Fixed Point Theory and Applications, 2013151 (2013) · Zbl 1293.54036
[15] Samet, B.; Vetro, C.; Vetro, P., Fixed point theorems for \(\alpha-\psi \)-contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications, 75, 4, 2154-2165 (2012) · Zbl 1242.54027 · doi:10.1016/j.na.2011.10.014
[16] Karapınar, E.; Samet, B., Generalized \(\alpha-\psi\) contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis, 2012 (2012) · Zbl 1252.54037 · doi:10.1155/2012/793486
[17] Salimi, P.; Karapınar, E., Suzuki-Edelstein type contractions via auxiliary functions, Mathematical Problems in Engineering, 2013 (2013) · Zbl 1299.47105 · doi:10.1155/2013/648528
[18] Berinde, M., Approximate fixed point theorems, Studia Universitatis Babeş-Bolyai, 51, 1, 11-25 (2006) · Zbl 1164.54028
[19] Hussain, N.; Amini-Harandi, A.; Cho, Y. J., Approximate endpoints for set-valued contractions in metric spaces, Fixed Point Theory and Applications, 2010 (2010) · Zbl 1202.54033
[20] Ariza-Ruiz, D.; Jiménez-Melado, A.; López-Acedo, G., A fixed point theorem for weakly Zamfirescu mappings, Nonlinear Analysis: Theory, Methods & Applications, 74, 5, 1628-1640 (2011) · Zbl 1217.54037 · doi:10.1016/j.na.2010.10.033
[21] Berinde, V., Some remarks on a fixed point theorem for Ćirić-type almost contractions, Carpathian Journal of Mathematics, 25, 2, 157-162 (2009) · Zbl 1249.54078
[22] Suzuki, T., A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136, 5, 1861-1869 (2008) · Zbl 1145.54026 · doi:10.1090/S0002-9939-07-09055-7
[23] Hussain, N.; Kutbi, M. A.; Salimi, P., Fixed point theory in alpha-psi-complete metric spaces with applications · Zbl 1429.54051
[24] Jachymski, J., The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society, 136, 4, 1359-1373 (2008) · Zbl 1139.47040 · doi:10.1090/S0002-9939-07-09110-1
[25] Hussain, N.; Al-Mezel, S.; Salimi, P., Fixed points for \(\psi \)-graphic contractions with application to integral equations, Abstract and Applied Analysis, 2013 (2013) · Zbl 1294.54026 · doi:10.1155/2013/575869
[26] Hussain, N.; Kutbi, M. A.; Salimi, P., Best proximity point results for modified \(\alpha-\psi \)-proximal rational contractions, Abstract and Applied Analysis (2013) · Zbl 1470.54065
[27] Hussain, N.; Khan, A. R.; Agarwal, R. P., Krasnosel’skii and Ky Fan type fixed point theorems in ordered Banach spaces, Journal of Nonlinear and Convex Analysis, 11, 3, 475-489 (2010) · Zbl 1219.47079
[28] Hussain, N.; Taoudi, M. A., Krasnosel’skii-type fixed point theorems with applications to Volterra integralequations, Fixed Point Theory and Applications, 2013, article 196 (2013) · Zbl 1302.47083
[29] Ansari, Q. H.; Idzik, A.; Yao, J.-C., Coincidence and fixed point theorems with applications, Topological Methods in Nonlinear Analysis, 15, 1, 191-202 (2000) · Zbl 1029.54047
[30] Nieto, J. J.; Rodríguez-López, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 3, 223-239 (2005) · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
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