Browse > Article
http://dx.doi.org/10.7858/eamj.2016.049

TRIPLED COINCIDENCE AND COMMON TRIPLED FIXED POINT THEOREM FOR HYBRID PAIR OF MAPPINGS SATISFYING NEW CONTRACTIVE CONDITION  

Deshpande, Bhavana (Department of Mathematics, Govt.B.S. P.G. College)
Handa, Amrish (Department of Mathematics, Govt.B.S. P.G. College)
Publication Information
East Asian mathematical journal / v.32, no.5, 2016 , pp. 701-716 More about this Journal
Abstract
We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.
Keywords
Tripled fixed point; tripled coincidence point; ${\omega}$-compatible mappings; F-weakly commuting mappings; new contractive condition;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 M. Abbas, L. Ciric, B. Damjanovic and M. A. Khan, Coupled coincidence point and common fixed point theorems for hybrid pair of mappings, Fixed Point Theory Appl. 1687-1812-2012-4.
2 S. M. Alsulami and A. Alotaibi, Tripled coincidence points for monotone operators in partially ordered metric spaces, International Mathematical Forum 7 (2012), no. 37, 1811-1824.
3 H. Aydi, E. Karapinar and M. Postolache, Tripled coincidence point theorems for weak ${\varphi}$-contractions in partially ordered metric spaces, Fixed Point Theory Appl. 44 (2012).
4 H. Aydi and E. Karapinar, Triple fixed points in ordered metric spaces, Bull. Math. Anal. Appl. 4 (2012), no. 1, 197-207.
5 H. Aydi and E. Karapinar, New Meir-Keeler type tripled fixed point theorems on partially ordered metric spaces, Mathematical Problems in Engineering, Volume 2012, Article ID 409872.
6 H. Aydi, E. Karapinar and C. Vetro, Meir-Keeler type contractions for tripled fixed points, Acta Math. Sci. 32B (2012), no. 6, 2119-2130.
7 V. Berinde, Coupled fixed point theorems for ${\varphi}$-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 75 (2012), 3218-3228.   DOI
8 V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), no. 15, 4889-4897.   DOI
9 V. Berinde and M. Borcut, Tripled coincidence theorems of contractive type mappings in partially ordered metric spaces, Appl. Math. Comput. 218 (2012), no. 10, 5929-5936.   DOI
10 T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), no. 7, 1379-1393.   DOI
11 B. Deshpande and A. Handa, Common coupled fixed point theorems for hybrid pair of mappings satisfying an implicit relation with application, Afr. Mat. 27 (2016), no. 1-2, 149-167.   DOI
12 P. Charoensawan, Tripled fixed points theorems of ${\varphi}$-contractive mixed monotone op-erators on partially ordered metric spaces, Applied Mathematical Sciences, 6 (2012), no. 105, 5229-5239.
13 B. Deshpande and A. Handa, Nonlinear mixed monotone-generalized contractions on partially ordered modified intuitionistic fuzzy metric spaces with application to integral equations, Afr. Mat. 26 (2015), no. 3-4, 317-343.   DOI
14 B. Deshpande and A. Handa, Application of coupled fixed point technique in solving integral equations on modified intuitionistic fuzzy metric spaces, Adv. Fuzzy Syst. Volume 2014, Article ID 348069.
15 B. Deshpande and A. Handa, Common coupled fixed point theorems for two hybrid pairs of mappings under ${\varphi}$-${\psi}$ contraction, ISRN Volume 2014, Article ID 608725.
16 B. Deshpande and A. Handa, Common coupled fixed point for hybrid pair of mappings under generalized non-linear contraction, East Asian Math. J. 31 (2015), no. 1, 77-89.   DOI
17 B. Deshpande and A. Handa, Common coupled fixed point theorems for hybrid pair of mappings under some weaker conditions satisfying an implicit relation, Nonlinear Analysis Forum 20 (2015), 79-93.
18 B. Deshpande and A. Handa, Common coupled fixed point theorems for two hybrid pairs of mappings satisfying an implicit relation, Sarajevo J. Math. 11 (23) (2015), no.1, 85-100.   DOI
19 B. Deshpande and A. Handa, Common coupled fixed point theorem under generalized Mizoguchi-Takahashi contraction for hybrid pair of mappings, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 22 (2015), no. 3, 199-214.
20 M. Abbas, H. Aydi and E. Karapinar, Tripled fixed point theorems for multivalued nonlin-ear contraction mappings in partially ordered metric spaces, Abstr. Appl. Anal. Volume 2011, Article ID 812690.
21 M. Abbas, B. Ali and A. Amini-Harandi, Common fixed point theorem for hybrid pair of mappings in Hausdorff fuzzy metric spaces, Fixed Point Theory Appl. 2012, 225.
22 B. Deshpande and A. Handa, Generalized Mizoguchi-Takahashi contraction in consideration of common tripled fixed point theorem for hybrid pair of mappings, Malaya J. Mat. 3 (2015), no. 1, 119-130.
23 B. Deshpande, S. Sharma and A. Handa, Tripled fixed point theorem for hybrid pair of mappings under generalized nonlinear contraction, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 21 (2014), no. 1, 23-38.
24 B. Deshpande, C. Kothari and A. Handa, Common tripled fixed point theorems under weaker conditions, IJPAM 103 (2015), no. 1, 1-17.
25 H. S. Ding, L. Li and S. Radenovic, Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 96.
26 D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), no. 5, 623-632.   DOI
27 V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), no. 12, 4341-4349.   DOI
28 W. Long, S. Shukla and S. Radenovic, Some coupled coincidence and common fixed point results for hybrid pair of mappings in 0-complete partial metric spaces, Fixed Point Theory Appl. 2013, 145.
29 N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011), 983-992.   DOI
30 M. Jain, K. Tas, S. Kumar and N. Gupta, Coupled common fixed point results involving a ${\varphi}$-${\psi}$ contractive condition for mixed g-monotone operators in partially ordered metric spaces, J. Inequal. Appl. 2012, 285.
31 J. T. Markin, Continuous dependence of fixed point sets, Proc. Amer. Math. Soc. 38 (1947), 545-547.
32 M. Mursaleen, S. A. Mohiuddine and R. P. Agarwal, Coupled fixed point theorems for alpha-psi contractive type mappings in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 228.
33 J. Rodriguez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets Syst. 147 (2004), 273-283.   DOI
34 B. Samet, E. Karapinar, H. Aydi and V. C. Rajic, Discussion on some coupled fixed point theorems, Fixed Point Theory Appl. 2013, 50.
35 N. Singh and R. Jain, Coupled coincidence and common fixed point theorems for set-valued and single-valued mappings in fuzzy metric space, Journal of Fuzzy Set Valued Analysis, Volume 2012, Year 2012 Article ID jfsva-00129, 10 pages.
36 W. Sintunavarat, P. Kumam and Y. J. Cho, Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory Appl. 2012, 170.