Browse > Article
http://dx.doi.org/10.7468/jksmeb.2019.26.4.289

UTILIZING ISOTONE MAPPINGS UNDER MIZOGUCHI-TAKAHASHI CONTRACTION TO PROVE MULTIDIMENSIONAL FIXED POINT THEOREMS WITH APPLICATION  

Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)
Publication Information
The Pure and Applied Mathematics / v.26, no.4, 2019 , pp. 289-303 More about this Journal
Abstract
We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Mizoguchi-Takahashi contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to integral equation. The results we obtain generalize, extend and unify several very recent related results in the literature.
Keywords
fixed point; Mizoguchi-Takahashi contraction; partially ordered metric space; non-decreasing mapping; mixed monotone mapping; integral equation;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 S.A. Al-Mezel, H. Alsulami, E. Karapinar & A. Roldan: Discussion on multidimensional coincidence points via recent publications. Abstr. Appl. Anal. 2014, Article ID 287492.
2 M. Berzig & B. Samet: An extension of coupled fixed point's concept in higher dimension and applications. Comput. Math. Appl. 63 (2012), no. 8, 1319-1334.   DOI
3 T.G. Bhaskar & V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), no. 7, 1379-1393.   DOI
4 L. Ciric, B. Damjanovic, M. Jleli & B. Samet: Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications. Fixed Point Theory Appl. 2012, 51.
5 B. Deshpande & A. Handa: Coincidence point results for weak ${\psi}-{\varphi}$ contraction on partially ordered metric spaces with application. Facta Universitatis Ser. Math. Inform. 30 (2015), no. 5, 623-648.
6 B. Deshpande, A. Handa & C. Kothari: Coincidence point theorem under Mizoguchi-Takahashi contraction on ordered metric spaces with application. IJMAA 3 (4-A) (2015), 75-94.
7 B. Deshpande, A. Handa & S.A. Thoker: Existence of coincidence point under generalized nonlinear contraction with applications. East Asian Math. J. 32 (2016), no. 1, 333-354.   DOI
8 B. Deshpande & A. Handa: On coincidence point theorem for new contractive condition with application. Facta Universitatis Ser. Math. Inform. 32 (2017), no. 2, 209-229.   DOI
9 B. Deshpande & A. Handa: Multidimensional coincidence point results for generalized $({\psi},{\theta},{\varphi})$-contraction on ordered metric spaces. J. Nonlinear Anal. Appl. 2017 (2017), no. 2, 132-143.   DOI
10 B. Deshpande & A. Handa: Utilizing isotone mappings under Geraghty-type contraction to prove multidimensional fixed point theorems with application. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 25 (2018), no. 4, 279-95.
11 W.S. Du: Coupled fixed point theorems for nonlinear contractions satisfied Mizoguchi-Takahashi's condition in quasi ordered metric spaces. Fixed Point Theory Appl. 2010, 9 (2010) Article ID 876372.
12 I.M. Erhan, E. Karapinar, A. Roldan & N. Shahzad: Remarks on coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory Appl. 2014, 207.
13 A. Roldan, J. Martinez-Moreno & C. Roldan: Multidimensional fixed point theorems in partially ordered metric spaces. J. Math. Anal. Appl. 396 (2012), 536-545.   DOI
14 J. Harjani, B. Lopez & K. Sadarangani: Fixed point theorems for mixed monotone operators and applications to integral equations. Nonlinear Anal. 74 (2011), 1749-1760.   DOI
15 E. Karapinar, A. Roldan, C. Roldan & J. Martinez-Moreno: A note on N-Fixed point theorems for nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2013, Article ID 310.
16 E. Karapinar, A. Roldan, J. Martinez-Moreno & C. Roldan: Meir-Keeler type multi-dimensional fixed point theorems in partially ordered metric spaces. Abstr. Appl. Anal. 2013, Article ID 406026.
17 A. Roldan & E. Karapinar: Some multidimensional fixed point theorems on partially preordered $G^{\ast}$ -metric spaces under $({\varphi},{\psi})$ -contractivity conditions. Fixed Point Theory Appl. 2013, Article ID 158.
18 A. Roldan, J. Martinez-Moreno, C. Roldan & E. Karapinar: Some remarks on multi-dimensional fixed point theorems. Fixed Point Theory 15 (2014), no. 2, 545-558.
19 F. Shaddad, M.S.M. Noorani, S.M. Alsulami & H. Akhadkulov: Coupled point results in partially ordered metric spaces without compatibility. Fixed Point Theory Appl. 2014, 204.
20 S.Wang: Coincidence point theorems for G-isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2013, 96.
21 S. Wang: Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces. Fixed Point Theory Appl. 2014, 137.