SOME FIXED POINT THEOREMS VIA CYCLIC CONTRACTIVE CONDITIONS IN S-METRIC SPACES

Gurucharan Singh Saluja

DOI Number
https://doi.org/10.22190/FUMI200811028S
First page
377
Last page
394

Abstract


We present some fixed point theorems for mappings which satisfy certain cyclic contractive conditions in the setting of $S$-metric spaces. The results presented in this paper generalize or improve many existing fixed point theorems in the literature. We also presented an application of our result to well-posed of fixed point problem. To support our results, we give some examples.

Keywords

Fixed point, cyclic contraction, S-metric space

Full Text:

PDF

References


bibitem{A09} M. Akkouchi, {it Weii-posedness of the fixed point problem for certain asymptotically regular mappings}, Annalas Math. Silesianae {bf 23} (2009), 43-52.

bibitem{AP10} M. Akkouchi and V. Popa, {it Weii-posedness of the fixed point problem for mappings satisfying an implicit relations}, Demonstr. Math. {bf 43(4)} (2010), 923-929.

bibitem{AZ18} A. H. Ansari and K. Zoto, {it Some fixed point theorems and cyclic contractions in dislocated quasi-metric spaces}, Facta Universitatis (NIS), Ser. Math. Inform. {bf 33(1)} (2018), 91-106.

bibitem{B22} S. Banach, {it Surles operation dans les ensembles

abstraits et leur application aux equation integrals}, Fund. Math.

{bf 3}(1922), 133-181.

bibitem{C72} S. K. Chatterjae, {it Fixed point theorems

compactes}, Rend. Acad. Bulgare Sci. {bf 25}(1972), 727-730.

bibitem{C12} C. M. Chen, {it Fixed point theorem for the cyclic weaker Meir-Keeler function in complete metric spaces}, Fixed Point Theory Appl. {bf 2012:17} (2012). doi:10.1186/1687-1812-2012-17.

bibitem{BV11} C. Di Bari and V. Popa, {it Fixed points for weak $varphi$-contractions on partial metric spaces}, Int. J. Engin. Contemp. Math. Sci. {bf 1} (2011), 5-13.

bibitem{DM89} F. S. De Blasi and J. Myjak, {it Sur la porosit$acute{e}$ des contractions sans point fixed}, C. R. Acad. Sci. Paris {bf 308} (1989), 51-56.

bibitem{G13} A. Gupta, {it Cyclic contraction on $S$-metric space}, Int. J. Anal. Appl. {bf 3(2)} (2013), 119-130.

bibitem{K69} R. Kannan, {it Some results on fixed point

theorems}, Bull. Calcutta Math. Soc. {bf 60}(1969), 71-78.

bibitem{K11} E. Karapinar, {it Fixed point theorem for cyclic weak $phi$-contraction}, Appl. Math. Lett. {bf 24} (2011), 822-825.

bibitem{KEU12} E. Karapinar, I. M. Erhan and A. Y. Ulus, {it Fixed point theorem for cyclic maps on partial metric spaces}, Appl. Math. Inf. Sci. {bf 6} (2012), 239-244.

bibitem{KN13} E. Karapinar and H. K. Nashine, {it Fixed point theorems for Kannan type cyclic weakly contractions}, J. Nonlinear Anal. Optim. {bf 4(1)} (2013), 29-35.

bibitem{KSV03} W. A. Kirk, P. S. Shrinavasan and P. Veeramani, {it fixed points for mappings satisfying cyclical contractive conditions}, Fixed Point Theory {bf 4} (2003), 79-89.

bibitem{LD05} B. K. Lahiri and P. Das, {it Well-posedness and porosity of a certain class of operators}, Demonstr. Math. {bf 38(1)} (2005), 169-176.

bibitem{NKR13} H. K. Nashine, Z. Kadelburg and S. Radenovi$acute{c}$, {it Fixed point theorems via various cyclic contractive conditions in partial metric spaces}, Publ. de L'Institut Mathematique, Nouvelle Serie, tome {bf 93(107)} (2013), 69-93.

bibitem{PR10} M. P$check{a}$curar and I. A. Rus, {it Fixed point theorem for cyclic $phi$-contractions}, Nonlinear Anal. {bf 72} (2010), 1181-1187.

bibitem{P10} M. A. Petric, {it Some results concerning cyclical contractive mappings}, General Math. {bf 18} (2010), 213-226.

bibitem{P11} M. A. Petric, {it Best proximity point theorems for weak cyclic Kannan contractions}, Filomat {bf 25(1)} (2011), 145-154.

bibitem{P06} V. Popa, {it Weii-posedness of fixed point problems in orbitally complete metric spaces}, Stud. Cerc. St. Ser. Mat. Univ. {bf 16} (2006), Supplement. Proceedings of ICMI 45, Bacau, Sept. 18-20 (2006), 209-214.

bibitem{P08} V. Popa, {it Weii-posedness of fixed point problems in compact metric spaces}, Bul. Univ. Petrol-Gaze, Ploiest, Sec. Mat. Inform. Fiz. {bf 60(1)} (2008), 1-4.

bibitem{RZ01} S. Reich and A. T. Zaslawski, {it Weii-posedness of fixed point problems}, Far East J. Math. Sci., Special Volume part III (2001), 393-401.

bibitem{R77} B. E. Rhoades, {it A comparison of various definitions of contractive mappings}, Trans. Amer. Math. Soc. {bf 333} (1977), 257-290.

bibitem{SSA12} S. Sedghi, N. Shobe and A. Aliouche, {it A generalization of fixed point theorems in $S$-metric spaces}, Mat. Vesnik {bf 64(3)} (2012), 258-266.

bibitem{SD14} S. Sedghi and N. V. Dung, {it Fixed point theorems on $S$-metric spaces}, Mat. Vesnik {bf 66(1)} (2014), 113-124.




DOI: https://doi.org/10.22190/FUMI200811028S

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)