Fixed Point Theorem Through Ω-distance of Suzuki Type Contraction Condition

Year 2016, Volume: 29 Issue: 1, 129 - 133, 21.03.2016

Wasfi Ahmed Shatanawi , Kamal K. Abodaye , Anwer Bataihah

Abstract

In this article, we utilize the notion of $\Omega$-distance in the sense of Saadati et al [R. Saadati, S.M. Vaezpour, P. Vetro and B.E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, {\it Mathematical and Computer Modeling,} \textbf{52}, 797-801, 2010] to introduce and prove some fixed point results of self-mapping under contraction conditions of the form $\Omega$-Suzuki-contractions.

Keywords

Ω-Distance , Fixed Point Theory , G-Metric Space

References

• Mustafa, Z. and Sims, B., “A new approach to generalized metric spaces”, J. Nonlinear Convex Anal.,7, no. 2: 289-297, (2006).
• Abbas, M., Shatanawi, W. and Nazir, T., “Common coupled coincidence and coupled fixed point of C- contractive mappings in generalized metric spaces”, Thai Journal of Mathematics, 13 (2): 339-353 (2015).
• Gu, F. and Shatanawi, W., “Common fixed point for generalized weakly G-contraction mappings satisfying com- mon (E.A) property in G-metric spaces”, Fixed Point Theory and Applications, 2013:309, 1-15, (2013).
• Aydi, H., Shatanawi, W. and Vetro, G., “On generalized weakly G-contraction mapping in G- metric spaces”, Comput.Math. Appl., 62:4222– 4229, (2011).
• Mustafa, Z. and Sims, B., “Fixed Point Theorems for contractive Mappings in Complete G-Metric Spaces”, Fixed Point Theory Appl., Hindawi Publishing Corporation, ID 917175, 10 pages, (2009).
• Mustafa, Z., Obedat, H. and Awawdeh, F., “Some fixed point theorems for mapping on complete G- metric spaces”, Fixed Point Theory and Applications, 2008, Artcle ID 189870, 12 pages, (2008).
• Mustafa, Z., Shatanawi, W. and Bataineh, M., “Existence of fixed point results in G-metric spaces”, International Jornal of Mathematics and Mathematical Sciences, Artcle ID 283028, 10 pages, (2009).
• Shatanawi, W., Chauhan, S.,Postolache, M., Abbas, M. and Radenovic, S., “Common fixed points for contractive mappings of integral type in G-metric space”, J. Adv. Math. Stud., 6(1): 53–72, (2013).
• Shatanawi, W. and Abbas, M., “Some fixed point results for multi valued mappings in ordered G- metric spaces”, Gazi University Journal of Science, 25: 385-392 (2012)
• Shatanawi, W. and Postolache, M., “Some fixed point results for a G-weak contraction in G-metric spaces”, Abstract and Applied Analysis, Article ID 815870, 19 pages, (2012).
• Jleli, M. and Samet, B., “Remarks on G -metric spaces and fixed point theorems”, Fixed Point Theory Appl., Article ID 210, (2012).
• Samet, B., Vetro, C. and Vetro, F., “Remarks on G -metric spaces”, Int. J. Anal., Article ID 917158 (2013).
• Saadati, R., Vaezpour, S. M., Vetro, P. and Rhoades, B. E., “Fixed point theorems in generalized partially ordered G-metric spaces”, Mathematical and Computer Modeling, 52: 797– 801, (2010).
• Gholizadeh, L., Saadati, R., Shatanawi, W. and Vaezpour, S. M., “Contractive mapping in generalized, ordered metric spaces with application in integral equations”, Math. Probl. Eng., Article ID 380784 (2011).
• Shatanawi, W. and Pitea, A., “Fixed and coupled fixed point theorems of Ω-distance for nonlinear contraction”, Applications, 2013:275, (2013). Theory and
• Shatanawi, W., Bataihah, A. and Pitea, A., “Fixed and common fixed point results for cyclic mappings of Ω-distance”, J. Nonlinear Sci. Appl., 9: 727– 735, (2016).
• Shatanawi, W. and Pitea, A., “Ω-Distance and coupled fixed point in G-metric spaces”, Fixed Point Theory and Applications, 2013:208, (2013).
• Suzuki, T., “A generalized Banach contraction principle that characterizes metric completeness”, Proc. Amer. Math.Soc., bf 136, 1861–1869,(2008).
• Khan, M. S., Swaleh, M. and Sessa, S., “Fixed point theorems by altering distances between the points”, Bull. Aust.Math. Soc., 30:1–9, (1984).