Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

  • Erdal KARAPINAR
  • Hassen AYDI
  • Zead MUSTAFA
Keywords: Tripled coincidence point, tripled common fixed point, ordered sets, metric spaces, generalized contractions.

Abstract

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

Author Biographies

Erdal KARAPINAR
Department ofMathematics, Atılım University, 06836,˙Incek, Ankara, Turkey.
Hassen AYDI
Université de Sousse, Institut Supérieur d’Informatique et des Technologies de Communication de Hammam Sousse. Route GP1-4011, H. Sousse, Tunisie.
Zead MUSTAFA
Department ofMathematics, The Hashemite University, P.O. 330127, Zarqa 13115, Jordan.

References

M. Abbas and H. Aydi, On common fixed point of generalized contractive mappings in metric spaces, Surveys in Mathematics and its Applications, 7(2012),

--47.

M. Abbas, H. Aydi and E. Karapinar, Tripled common fixed point in partially ordered metric spaces, submitted.

M. Abbas, M. A. Khan and S. Radenovic, Common coupled fixed point theorem in cone metric space for $w-$compatible mappings, Appl. Math. Comput. 217(2010), 195--202.

Ya.I. Alber and S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Operator Theory, in: Advances and Appl. 98, user, Basel, (1997), 7--22.

I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. Volume 2010 (2010). Article ID 621492.

H. Aydi, Coincidence and common fixed point results for contraction type maps in partially ordered metric spaces, Int. Journal of Math. Analysis, Volume 5 (13) (2011),631--642.

H. Aydi, Some coupled fixed point results on partial metric spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2011, Article ID 647091, 11 pages.

H. Aydi, A common fixed point result for a $(psi,varphi)$-weak contractive condition type, Journal of Applied Mathematics and Informatics, 30 (5-6) (2012), 809--820.

H. Aydi, B. Samet and C. Vetro, Coupled fixed point results in cone metric spaces for $tilde{w}$-compatible mappings, Fixed Point Theory Appl., 2011, 2011:27.

V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9 (1) (2004), 43--53.

V. Berinde, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math., 24 (2)(2008), 10--19.

V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (15) (2011), 4889--4897.

I. Beg and M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory Appl., 2006 (2006). Article ID 74503.

T. G. Bhaskar and V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379--1393.

C. E. Chidume, H. Zegeye and S.J. Aneke, Approximation of fixed points of weakly contractive non self maps in Banach spaces, J. Math. Anal. Appl., 270 (1)(2002),189--199.

Binayak S. Choudhury and N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear Anal., 72(2010), 1589--1593.

Binayak S. Choudhury, N. Metiya and A. Kundu, Coupled coincidence point theorems in ordered metric spaces, Ann. Univ. Ferrara., 57 (2011), 1--16.

B.S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal.,73 (2010), 2524--2531.

J. Harjani and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71 (2009), 3403--3410.

E. Karapi nar, Couple fixed point on cone metric spaces, Gazi University Journal of Science, 24 (1)(2011), 51--58.

E. Karapi nar, Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59 (12) (2010), 3656--3668.

E. Karapinar, Fixed point theory for cyclic weak $phi$-contraction, Appl. Math. Lett., 24(6) (2011), 822--825.

V. Lakshmikantham and Lj. B. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70(2009), 341--4349.

N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal., 74(2011), 983--992.

H. K. Nashine, H. Aydi, Generalized altering distances and common fixed points in ordered metric spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2012, Article ID 736367, 23 pages.

H. K. Nashine and H. Aydi, Common fixed point theorems for four mappings through generalized altering distances in ordered metric spaces, Annali dell'Universita di Ferrara, doi : 10.1007/s11565-012-0151-y, (2012).

H.K. Nashine and B. Samet, Fixed point results for mappings satisfying $(psi,phi)$-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74(2011), 2201--2209.

J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223--239.

A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435--1443.

B.E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (4) (2001), 2683--2693.

B. Samet, Coupled fixed point theorems for a generalized Meir Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 7(12)(2010), 4508--4517.

B. Samet and C. Vetro, Coupled fixed point, $f$-invariant set and fixed point of $N$-order, Ann. Funct. Anal., 1 (2)(2010), 46--56.

Y. Song, Coincidence points for noncommuting $f$-weakly contractive mappings, Int. J. Comput. Appl. Math., 2 (1)(2007), 51--57.

Published
2012-09-21
How to Cite
KARAPINAR, E., AYDI, H., & MUSTAFA, Z. (2012). Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces. Tamkang Journal of Mathematics, 44(3), 233-251. https://doi.org/10.5556/j.tkjm.44.2013.990
Section
Papers