Fixed point theorems in <em>R</em>-metric spaces with applications

Siamak Khalehoghli; Hamidreza Rahimi; Madjid Eshaghi Gordji; Siamak Khalehoghli; Hamidreza Rahimi; Madjid Eshaghi Gordji

doi:10.3934/math.2020201

AIMS Mathematics

2020, Volume 5, Issue 4: 3125-3137. doi: 10.3934/math.2020201

Previous Article Next Article

Research article

Fixed point theorems in R-metric spaces with applications

1.
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2.
Department of Mathematics, Semnan University, Semnan, Iran

Received: 24 October 2019 Accepted: 10 March 2020 Published: 24 March 2020
MSC : 54H25, 47H10

The purpose of this paper is to introduce the notion of R-metric spaces and give a real generalization of Banach fixed point theorem. Also, we give some conditions to construct the Brouwer fixed point. As an application, we find the existence of solution for a fractional integral equation.
- R-metric spaces,
- fixed point,
- strong R-compact metric spaces,
- fractional integral equations
Citation: Siamak Khalehoghli, Hamidreza Rahimi, Madjid Eshaghi Gordji. Fixed point theorems in R-metric spaces with applications[J]. AIMS Mathematics, 2020, 5(4): 3125-3137. doi: 10.3934/math.2020201

Related Papers:

Abstract

The purpose of this paper is to introduce the notion of R-metric spaces and give a real generalization of Banach fixed point theorem. Also, we give some conditions to construct the Brouwer fixed point. As an application, we find the existence of solution for a fractional integral equation.

References

[1]	C. T. Aage, J. N. Salunke, Fixed points of weak contractions in cone metric spaces, Ann. Funct. Anal., 2 (2011), 71.
[2]	M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420.
[3]	A. N. Abdou, M. A. Khamsi, Fixed point results of pointwise contractions in modular metric spaces, Fixed Point Theory Appl., (2013), 163.
[4]	S. Aleksic, Z. Kadelburg, Z. D. Mitrovic, et al. A new survey: Cone metric spaces, J. Int. Math. Virtual Institute., 9 (2019), 93-121.
[5]	H. Baghani, M. E. Gordji, M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl., 18 (2016), 465-477. doi: 10.1007/s11784-016-0297-9
[6]	S. Banach, Sur les operations dans les ensembles abstrits et leur applications aux equations integrals, Fund. Math., 3 (1922), 133-181.
[7]	L. E. Brouwer, Uber Abbildung von Mannigfaltigkeiten, Math Ann., 71 (1912), 97-115.
[8]	V. V. Chistyakov, Modular metric spaces, I: basic concepts, Nonlinear Anal., 72 (2010), 1-14.
[9]	V. V. Chistyakov, Modular metric spaces, II: application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
[10]	S. H. Cho, J. S. Bae, Fixed point theorems for multivalued maps in cone metric spaces, Fixed Point Theory Appl., 2011 (2011), Article number: 87.
[11]	L. Ciric, Some Recent Results in Metrical Fixed Point Theory, University of Belgrade, Beograd, 2003.
[12]	G. Deng, H. Huang, M. Cvetkovic, et al. Cone valued measure of noncompactness and related fixed point theorems, Bull. Int. Math. Virtual Inst., 8 (2018), 233-243.
[13]	M. Eshaghi Gordji, H Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algeb., 6 (2017), 251-260.
[14]	M. Eshaghi Gordji, M. Ramezani, M. De La Sen, et al. On orthogonal sets and Banach fixed point theorem, Fixed Point Theory., 18 (2017), 569-578. doi: 10.24193/fpt-ro.2017.2.45
[15]	L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.
[16]	D. Ilic, V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), 876-882. doi: 10.1016/j.jmaa.2007.10.065
[17]	S. Kakutani, A generalization of Brouwer fixed point theorem, Duke Math. J., 8 (1941), 457-459. doi: 10.1215/S0012-7094-41-00838-4
[18]	M. A. Khamsi, W. K. Kozlowski, S. Reich, Fixed point theory in modular function spaces, Nonlinear Anal., 14 (1990), 935-953.
[19]	M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129.
[20]	W. Kirk, N. Shahzad, Fixed Point Theory in Disatnce Spaces, Springer International Publishing Switzeralan, 2014.
[21]	N. Mehmood, A. Al Rawashdeh, S. Radenovic, New fixed point results for E-metric spaces, Positivity, 23 (2019), 1101-1111.
[22]	S. B. Nadler, Multi-valued contraction mappings, Pacific J. Mafh., 30 (1969), 475-488.
[23]	F. J. Nash, Equilibrium points in n-person game, Proc. Natl. Acad. Sci. USA., 36 (1950), 48-49. doi: 10.1073/pnas.36.1.48
[24]	J. J. Nieto, R. Rodri Guez-Lo'Pez, Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations, Order 22 (2005), 223-239.
[25]	M. A. Noor, An iterative algorithm for variational inequalities, J. Math. Anal. Appl., 158 (1991), 448-455.
[26]	Z. Pales, I-R. Petre, Iterative fixed point theorems in E-metric spaces, Acta Math. Hung., 140 (2013), 134-144.
[27]	E. De Pascale, G. Marino, P. Pietramala, The use of the E-metric spaces in the search for fixed points, Matematiche, 48 (1993), 367-376.
[28]	M. Ramezani, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), 127-132.
[29]	M. Ramezani, H. Baghani, Contractive gauge functions in strongly orthogonal metric spaces, Int. J. Nonlinear Anal. Appl., 8 (2017), 23-28.
[30]	A. C. M. Ran, 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.
[31]	A. Al-Rawashdeh, W. Shatanawi, M. Khandaqji, Normed ordered and E-metric spaces, Int. J. Math. Sci., 2012 (2012), ID 272137.
[32]	W. Rudin, Principles of mathematical analysis, thired edition, McGraw-Hill, Inc, 1976.
[33]	V. Todorcevic, Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics, Springer Nature Switzerland AG, 2019.
[34]	D. Turkoglu, M. Abuloha, A. bdeljawad T: KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Anal., 72 (2010), 348-353.

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)