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

Volume 18, Issue 2, pp 184--191 Publication Date: January 28, 2018       Article History
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### 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.

### Keywords

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

•  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.

• [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.

• [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.