On Suzuki-Wardowski type fixed point theorems

Volume 8, Issue 6, pp 1095--1111 http://dx.doi.org/10.22436/jnsa.008.06.19

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Authors

Nawab Hussain - Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. Jamshaid Ahmad - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan. Akbar Azam - Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.

Abstract

Recently, Piri and Kumam [Fixed Point Theory and Applications 2014, 2014:210] improved concept of F- contraction and proved some Wardowski and Suzuki type fixed point results in metric spaces. The aim of this article is to define generalized \(\alpha-GF\)-contraction and establish Wardowski and Suzuki type fixed point results in metric and ordered metric spaces and derive main results of Piri et al. as corollaries. We also deduce certain fixed and periodic point results for orbitally continuous generalized F-contractions and certain fixed point results for integral inequalities are derived. Moreover, we discuss some illustrative examples to highlight the realized improvements.

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Keywords

• Fixed point
• \(\alpha-GF\)-contraction
• \(\alpha-\eta\)-continuous function
• orbitally continuous function.

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl., 2013 (2013), 11 pages.


• [2] R. P. Agarwal, N. Hussain, M. A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstr. Appl. Anal., 2012 (2012), 15 pages.


• [3] Q. H. Ansari, A. Idzik, J. C. Yao, Coincidence and fixed point theorems with applications , Topol. Methods Nonlinear Anal., 15 (2000), 191-202.


• [4] S. Banach, Sur les opérations dans les ensembles abstraits et leur applications aux équations intégrales, Fundam. Math., 3 (1922), 133-181.


• [5] D. Dorić, Z. Kadelburg, S. Radenović , Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces, Nonlinear Anal., 75 (2012), 1927-1932.


• [6] S. Fathollahi, N. Hussain, L. A. Khan, Fixed point results for modified weak and rational \(\alpha-\psi\)-contractions in ordered 2-metric spaces, Fixed Point Theory Appl., 2014 (2014), 25 pages.


• [7] N. Hussain, S. Al-Mezel, P. Salimi , Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl Anal., 2013 (2013), 11 pages.


• [8] N. Hussain, D. Dorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages.


• [9] N. Hussain, E. Karapinar, P. Salimi, F. Akbar, \(\alpha\)-admissible mappings and related fixed point theorems, J. Inequal. Appl., 2013 (2013), 11 pages.


• [10] N. Hussain, M. A. Kutbi, S. Khaleghizadeh, P. Salimi, Discussions on recent results for \(\alpha-\psi\)-contractive mappings, Abst. Appl. Anal., 2014 (2014), 13 pages.


• [11] N. Hussain, M. A. Kutbi, P. Salimi , Best proximity point results for modified \(\alpha-\psi\)-proximal rational contractions , Abstr. Appl. Anal., 2013 (2013), 14 pages.


• [12] N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in \(\alpha\)-complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 11 pages.


• [13] N. Hussain, A. Latif, P. Salimi , Best proximity point results for modified Suzuki \(\alpha-\psi\)-proximal contractions, Fixed Point Theory Appl., 2014 (2014), 16 pages.


• [14] N. Hussain, P. Salimi , Suzuki-Wardowski type fixed point theorems for \(\alpha-GF\)-contractions , Taiwanese J. Math., 18 (2014), 1879-1895.


• [15] N. Hussain, M. A. Taoudi, Krasnosel'skii-type fixed point theorems with applications to Volterra integral equations , Fixed Point Theory Appli., 2013 (2013), 16 pages.


• [16] S. K. Malhotra, S. Radenović, S. Shukla, Some fixed point results without monotone property in partially ordered metric spaces, J. Egyptian Math. Soc., 22 (2014), 83-89.


• [17] J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-229.


• [18] H. Piri, P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 16 pages.


• [19] S. Radenović, Z. Kadelburg, D. Jandrlić, A. Jandrlić, Some results on weakly contractive maps, Bull. Iranian Math. Soc., 38 (2012), 625-645.


• [20] V. C. Rajić, S. Radenović, W. Shatanawi, N. Tahat, Common fixed point results for weakly isotone increasing mappings in partially ordered partial metric spaces, The Matematiche, 68 (2013), 191-204.


• [21] P. Salimi, A. Latif, N. Hussain, Modified \(\alpha-\psi\)-contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 19 pages.


• [22] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154-2165.


• [23] N. A. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl., 2013 (2013), 13 pages.


• [24] M. Sgroi, C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, 27 (2013), 1259-1268.


• [25] S. Shukla, S. Radenović, Some common fixed point theorems for F-contraction type mappings in 0-complete partial metric spaces, J. Math., 2013 (2013), 7 pages.


• [26] T. Suzuki , A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317.


• [27] T. Suzuki , A generalized Banach contraction principle that characterizes metric completeness , Proc. Amer. Math. Soc., 136 (2008), 1861-1869.


• [28] W. Takahashi, L. J. Lin, S. Y. Wang, Fixed point theorems for contractively generalized hybrid mappings in complete metric spaces, J. Nonlinear Convex Anal., 13 (2012), 195-206.


• [29] D. Wardowski , Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 6 pages.


• [30] D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric space, Demonstr. Mathe., 47 (2014), 10 pages.