Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces

Volume 18, Issue 2, pp 184--191 http://dx.doi.org/10.22436/jmcs.018.02.06

Publication Date: January 28, 2018 Submission Date: August 11, 2017

Download PDF

Download XML

1552 Downloads
2159 Views

Authors

Kanayo Stella Eke - Department of Mathematics, Covenant University, Canaanland, KM 10 Idiroko Road, P. M. B. 1023, Ota, Ogun State, Nigeria Bijan Davvaz - Department of Mathematics, Yazd University, Yazd, Iran Jimevwo Godwin Oghonyon - Department of Mathematics, Covenant University, Canaanland, KM 10 Idiroko Road, P. M. B. 1023, Ota, Ogun State, Nigeria

Abstract

In this paper, we introduce a class of nonlinear contractive mappings in metric space. We also establish common fixed point theorems for these pair of non-self mappings satisfying the new contractive conditions in the convex metric space . An example is given to validate our results. The results generalize and extend some results in literature.

Share and Cite

ISRP Style

Kanayo Stella Eke, Bijan Davvaz, Jimevwo Godwin Oghonyon, Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces, Journal of Mathematics and Computer Science, 18 (2018), no. 2, 184--191

AMA Style

Eke Kanayo Stella, Davvaz Bijan, Oghonyon Jimevwo Godwin, Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces. J Math Comput SCI-JM. (2018); 18(2):184--191

Chicago/Turabian Style

Eke, Kanayo Stella, Davvaz, Bijan, Oghonyon, Jimevwo Godwin. "Common fixed point theorems for non-self mappings of nonlinear contractive maps in convex metric spaces." Journal of Mathematics and Computer Science, 18, no. 2 (2018): 184--191

Keywords

Convex metric space
nonlinear contractive mapping
non-self mapping
common fixed point
coincidentally commuting

MSC

47H10

References

[1] M. Abbas, J. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416–420.

[2] T. Abdeljawad, E. Karapınar, K. Taş, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904.

[3] H. Akewe, G. A. Okeke, Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive -like operators, J. Fixed Point Theory Appl., 2015 (2015), 8 pages.

[4] N. A. Assad , On a fixed point theorem in Banach space, Tamkang J. Math., 7 (1976), 91–94.

[5] N. A. Assad, W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math., 43 (1972), 553–562.

[6] H. Aydi, A. Felhi, E. Karapınar, On common best proximity points for generalized alpha-psi-proximal contraction, J. Nonlinear Sci. Appl., 9 (2016), 2658–2670.

[7] H. Aydi, M. Jellahi, E. Karapinar, Common fixed points for generalized \(\alpha\)- implicit contractions in partial metric spaces: consequences and application, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 109 (2015), 367–384.

[8] L. B. Ćirić, Contractive-type non-self mappings on metric spaces of hyperbolic type, J. Math. Anal. Appl., 317 (2006), 28–42.

[9] L. Ćirić, V. Rakočević, S. Radenović, M. Rajović, R. Lazović, Common fixed point theorems for non-self mappings in metric spaces of hyperbolic type, J. Comput. Appl. Math. , 233 (2010), 2966–2974.

[10] L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476.
- View Article
- Google Scholar

[11] M. Imdad, S. Kumar, Rhoades-type fixed-point theorems for a pair of nonself mappings, Comput. Math. Appl., 46 (2003), 919–927

[12] E. Karapınar, A note on common fixed point theorem in partial metric spaces, Miskolic Math. Notes, 12 (2011), 185–191.
- MathSciNet

[13] W. A. Kirk, Krasnoselskii’s iteration process in hyperbolic space, Numer. Funct. Anal. Optim., 4 (1982), 371–381.

[14] G. A. Okeke, M. Abbas, Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator, J. Inequal. Appl., 2015 (2015 ), 11 pages.

[15] G. A. Okeke, J. K. Kim, Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process, J. Inequal. Appl., 2015 (2015 ), 14 pages.

[16] S. Radenović, B. E. Rhoades, Fixed point theorem for two non-self mappings in cone metric spaces, Comput. Math. Appl., 57 (2009), 1701–1707.

[17] B. E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon., 23 (1978), 457–459.

[18] R. Sumitra, V. R. Uthariaraj, R. Hemavathy, P. Vijayaraju, Common fixed point theorem for non-self mappings satisfying generalized Ciric type contraction condition in cone metric space, J. Fixed Point Theory Appl., 2010 (2010 ), 17 pages.

[19] W. Takahashi, A convexity in metric spaces and nonexpansive mappings, I, Kodai Math. Sem. Rep., 22 (1970), 142–149.