MULTIDIMENSIONAL FIXED POINT RESULTS FOR CONTRACTION MAPPING PRINCIPLE WITH APPLICATION

Amrish Handa

DOI Number
https://doi.org/10.22190/FUMI2004919H
First page
919
Last page
928

Abstract


The main aim of this article is to study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under contraction mapping principle 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 an integral equation. The results we obtain generalize, extend and unify several classical and very recent related results in the literature in metric spaces.


Keywords

fixed point, contraction mapping principle, partially ordered metric space, non-decreasing mapping, integral equation.

Full Text:

PDF

References


S.M. Alsulami, Some coupled coincidence point theorems for a mixed monotone operator in a complete metric space endowed with a partial order by using altering distance functions, Fixed Point Theory Appl. 2013, 194.

M. Berzig and B. Samet, An extension of coupled fixed point's concept in higher dimension and applications, Comput. Math. Appl. 63 (8) (2012), 1319--1334.

B. Deshpande, and A. Handa, Coincidence point results for weak ψ-ϕ contraction on partially ordered metric spaces with application, Facta Universitatis Ser. Math. Inform. 30 (5) (2015), 623--648.

B. Deshpande, A. Handa and C. Kothari, Coincidence point theorem under Mizoguchi-Takahashi contraction on ordered metric spaces with application, IJMAA 3 (4-A) (2015), 75-94.

B. Deshpande, A. Handa and S. A. Thoker, Existence of coincidence point under generalized nonlinear contraction with applications, East Asian Math. J. 32 (1) (2016), 333-354.

B. Deshpande and A. Handa, On coincidence point theorem for new contractive condition with application, Facta Universitatis Ser. Math. Inform. 32 (2) (2017), 209--229.

B. Deshpande and A. Handa, Multidimensional coincidence point results for generalized (ψ, θ, ϕ)-contraction on ordered metric spaces, J. Nonlinear Anal. Appl. 2017 (2) (2017), 132-143.

B. Deshpande, and 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 (4) (2018), 279-95.

I.M. Erhan, E. Karapinar, A. Roldan and N. Shahzad, Remarks on coupled coincidence point results for a generalized compatible pair with applications, Fixed Point Theory Appl. 2014, 207.

E. Karapinar, A. Roldan, J. Martinez-Moreno and C. Roldan, Meir-Keeler type multidimensional fixed point theorems in partially ordered metric spaces, Abstr. Appl. Anal. 2013, Article ID 406026.

S.A. Al-Mezel, H. Alsulami, E. Karapinar and A. Roldan, Discussion on multidimensional coincidence points via recent publications, Abstr. Appl. Anal. Volume 2014, Article ID 287492.

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

J.J. Nieto, R.L. Pouso and R. Rodriguez-Lopez, Fixed point theorems in partially ordered sets, Proc. Amer. Math. Soc. 132 (8) (2007), 2505-2517.

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

A. Razani and V. Parvaneh, Coupled coincidence point results for (ψ, α, β)-weak contractions in partially ordered metric spaces, J. Appl. Math. 2012, Article ID 496103 (2012).

A. Roldan, J. Martinez-Moreno and C. Roldan, Multidimensional fixed point theorems in partially ordered metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545.

A. Roldan, J. Martinez-Moreno, C. Roldan and E. Karapinar, Multidimensional fixed-point theorems in partially ordered complete partial metric spaces under (ψ, ϕ)-contractivity conditions, Abstr. Appl. Anal. vol. 2013, Article ID 634371.

A. Roldan, J. Martinez-Moreno, C. Roldan and E. Karapinar, Some remarks on multidimensional fixed point theorems, Fixed Point Theory 15 (2) (2014), 545-558.

F. Shaddad, M.S.M. Noorani, S.M. Alsulami and H. Akhadkulov, Coupled point results in partially ordered metric spaces without compatibility, Fixed Point Theory and Applications 2014, 204.

Y. Su, Contraction mapping principle with generalized altering distance function in ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl. 2014, 227.

S. Wang, Coincidence point theorems for G-isotone mappings in partially ordered metric spaces, Fixed Point Theory Appl. (2013), 1687-1812-2013-96.

S. Wang, Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces, Fixed Point Theory Appl. 2014, 137.




DOI: https://doi.org/10.22190/FUMI2004919H

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)