Fixed point results for dominated mappings in rectangular <em>b</em>-metric spaces with applications

Abdullah Shoaib; Tahair Rasham; Giuseppe Marino; Jung Rye Lee; Choonkil Park; Abdullah Shoaib; Tahair Rasham; Giuseppe Marino; Jung Rye Lee; Choonkil Park

doi:10.3934/math.2020335

AIMS Mathematics

2020, Volume 5, Issue 5: 5221-5229. doi: 10.3934/math.2020335

Previous Article Next Article

Research article

Fixed point results for dominated mappings in rectangular b-metric spaces with applications

1.
Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan
2.
Department of Mathematics, International Islamic University, H-10, Islamabad 44000, Pakistan
3.
Dipartimento di Matematica e Informatica, Universita della Calabria, 87036, Arcavacata di Rende (CS), Italy
4.
Department of Mathematics, Daejin University, Kyunggi 11159, Korea
5.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 06 March 2020 Accepted: 08 June 2020 Published: 17 June 2020
MSC : 46S40, 47H10, 54H25

In this paper, we establish some fixed point results for α-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular b-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular b-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established.
- fixed point,
- complete rectangular b-metric space,
- α-dominated mapping,
- Ćirić type rational contraction condition,
- partial order,
- $\preceq$-dominated mapping,
- graph dominated mapping
Citation: Abdullah Shoaib, Tahair Rasham, Giuseppe Marino, Jung Rye Lee, Choonkil Park. Fixed point results for dominated mappings in rectangular b-metric spaces with applications[J]. AIMS Mathematics, 2020, 5(5): 5221-5229. doi: 10.3934/math.2020335

Related Papers:

Abstract

In this paper, we establish some fixed point results for α-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular b-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular b-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established.

References

[1]	A. S. M. Alofi, A. E. Al-Mazrooei, B. T. Leyew, et al. Common fixed points of α-dominated multivalued mappings on closed balls in a dislocated quasi b-metric space, J. Nonlinear Sci. Appl., 10 (2017), 3456-3476. doi: 10.22436/jnsa.010.07.10
[2]	M. Arshad, Z. Kadelburg, S. Radenović, et al. Fixed points of α-dominated mappings on dislocated quasi metric spaces, Filomat, 31 (2017), 3041-3056. doi: 10.2298/FIL1711041A
[3]	M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space, Fixed Point Theory A., 2013 (2013), 1-15. doi: 10.1186/1687-1812-2013-1
[4]	M. Balaj, S. Muresan, A note on a Ćirić's fixed point theorem, Fixed Point Theory, 4 (2003), 237-240.
[5]	P. Baradol, D. Gopal, S. Radenović, Computational fixed point in graphical rectangular metric space, J. Comptut. Appl. Math., 375 (2020), 112805.
[6]	P. Baradol, J. Vujaković, D. Gopal, et al. On some new results in graphical rectangular b-metric spaces, Mathematics, 8 (2020), 488.
[7]	F. Bojor, Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal-theor., 75 (2012), 3895-3901. doi: 10.1016/j.na.2012.02.009
[8]	M. De la Sen, N. Nikolić, T. Došenović, et al. Some results on (s-q) graphic contraction mappings in b-metric-like spaces, Mathematics, 7 (2019), 1190.
[9]	H. S. Ding, M. Imdad, S. Radenović, et al. On some fixed point results in b-metric, rectangular and b-rectangular metric spaces, Arab Journal of Mathematical Sciences, 22 (2016), 151-164. doi: 10.1016/j.ajmsc.2015.05.003
[10]	N. V. Dung, The metrization of rectangular b-metric spaces, Topol. Appl., 261 (2019), 22-28. doi: 10.1016/j.topol.2019.04.010
[11]	R. George, S. Radenović, K. P. Reshma, et al. Rectangular b-metric space and contraction principles, J. Nonlinear Sci. Appl., 8 (2015), 1005-1013. doi: 10.22436/jnsa.008.06.11
[12]	N. Hussain, M. Arshad, A. Shoaib, et al. Common fixed point results for α-ψ-contractions on a metric space endowed with graph, J. Inequal. Appl., 2014 (2014), 136.
[13]	J. Jachymski, The contraction principle for mappings on a metric space with a graph, P. Am. Math. Soc., 136 (2008), 1359-1373.
[14]	R. Klén, V. Manojlović, S. Simić, et al. Bernouli inequality and hypergeometric function, P. Am. Math. Soc., 142 (2014), 559-573.
[15]	E. Malkowski, V. Rakočević, Advanced Functional Analysis, CRS Press, 2019.
[16]	A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, P. Am. Math. Soc., 132 (2004), 1435-1443. doi: 10.1090/S0002-9939-03-07220-4
[17]	A. Shoaib, α-ν Dominated mappings and related common fixed point results in closed ball, J. Concr. Appl. Math., 13 (2015), 152-170.
[18]	J. Tiammee, S. Suantai, Coincidence point theorems for graph-preserving multi-valued mappings, Fixed Point Theory A., 2014 (2014), 1-11. doi: 10.1186/1687-1812-2014-1
[19]	V. Todorčević, Harmonic Quasiconformol Mappings and Hyperbolic Type Metrics, Springer, 2019.
[20]	M. Younis, D. Singh, A. Goyal, A novel approach of graphical rectangular b-metric spaces with an application to the vibrations of a vertical heavy hanging cable, J. Fix. Point Theory A., 21 (2019), 33.
[21]	M. Younis, D. Singh, A. Petrusel, Applications of graph Kannan mappings to the damped springmass system and deformation of an elastic beam, Discrete Dyn. Nat. Soc., 2019 (2019), 1-9.

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)