Interpolative Hardy Roger's type contraction on a closed ball in ordered dislocated metric spaces and some results

Abdullah Shoaib; Poom Kumam; Kanokwan Sitthithakerngkiet; Abdullah Shoaib; Poom Kumam; Kanokwan Sitthithakerngkiet

doi:10.3934/math.2022762

AIMS Mathematics

2022, Volume 7, Issue 8: 13821-13831. doi: 10.3934/math.2022762

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Research article

Interpolative Hardy Roger's type contraction on a closed ball in ordered dislocated metric spaces and some results

1.
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
2.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
3.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), 1518, Wongsawang, Bangsue, Bangkok 10800, Thailand

Received: 13 March 2022 Revised: 28 April 2022 Accepted: 05 May 2022 Published: 23 May 2022
MSC : 54H25, 47H10

The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).
- dominated mappings,
- common fixed point,
- interpolative Hardy Roger's type contraction,
- closed ball,
- ordered dislocated metric spaces
Citation: Abdullah Shoaib, Poom Kumam, Kanokwan Sitthithakerngkiet. Interpolative Hardy Roger's type contraction on a closed ball in ordered dislocated metric spaces and some results[J]. AIMS Mathematics, 2022, 7(8): 13821-13831. doi: 10.3934/math.2022762

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Abstract

The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).

References

[1]	C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Appl. Math. Sci, 2 (2008), 2941–2948.
[2]	M. Abbas, S. Z. Németh, Finding solutions of implicit complementarity problems by isotonicity of the metric projection, Nonlinear Anal., 75 (2012), 2349–2361. https://doi.org/10.1016/j.na.2011.10.033 doi: 10.1016/j.na.2011.10.033
[3]	A. E. Al-Mazrooei, A. Shoaib, J. Ahmad, Cyclic $b$ -multiplicative $(A, B)$-Hardy-Rogers-type local contraction and related results in $b$-multiplicative and $b$-metric spaces, J. Math., 2020 (2020), 1–9. https://doi.org/10.1155/2020/2460702 doi: 10.1155/2020/2460702
[4]	A. E. Al-Mazrooei, A. Shoaib, J. Ahmad, Unique fixed-point results for $\beta $-admissible mapping under $\left(\beta -\psi \right) $ -contraction in complete dislocated $G_{d}$-metric space, Mathematics, 8 (2020), 1–13. https://doi.org/10.3390/math8091584 doi: 10.3390/math8091584
[5]	M. U. Ali, H. Aydi, M. Alansari, New generalizations of set valued interpolative Hardy-Rogers type contractions in b-metric spaces, J. Funct. Spaces, 2021 (2021), 1–8. https://doi.org/10.1155/2021/6641342 doi: 10.1155/2021/6641342
[6]	M. Arshad, A. Shoaib, P. Vetro, Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered dislocated metric spaces, J. Funct. Space., 2013 (2013), 1–9. https://doi.org/10.1155/2013/638181 doi: 10.1155/2013/638181
[7]	M. Arshad, A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered dislocated metric space, Fixed Point Theory A., 2013 (2013), 1–15. https://doi.org/10.1186/1687-1812-2013-115 doi: 10.1186/1687-1812-2013-115
[8]	J. P. Aubin, Mathematical methods of games and economic theory, Elsevier, North-Holland, Amsterdam, 1979.
[9]	H. Aydi, E. Karapınar, A. F. Roldán López de Hierro, $\omega $-interpolative Ćirić-Reich-Rus-type contractions, Mathematics, 7 (2019). https://doi.org/10.3390/math7010057 doi: 10.3390/math7010057
[10]	H. Aydi, C. M. Chen, E. Karapınar, Interpolative Ćirić-Reich-Rus type contractions via the Branciari distance, Mathematics, 7 (2019). https://doi.org/10.3390/math7010084 doi: 10.3390/math7010084
[11]	A. Arif, M. Nazam, Hussain, M. Abbas, The ordered implicit relations and related fixed point problems in the cone $b$-metric spaces, AIMS Math., 7 (2022), 5199–5219. https://doi.org/10.3934/math.2022290 doi: 10.3934/math.2022290
[12]	I. Beg, A. R. Butt, Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces, Math. Commun., 15 (2010), 65–76.
[13]	I. Beg, A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699–3704. https://doi.org/10.1016/j.na.2009.02.027 doi: 10.1016/j.na.2009.02.027
[14]	T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393. https://doi.org/10.1016/j.na.2005.10.017 doi: 10.1016/j.na.2005.10.017
[15]	S. Bohnenblust, S. Karlin, Contributions to the theory of games, Princeton University Press, Princeton, 1950.
[16]	L. B. Ćirić, Common fixed point theorems for set-valued mappings, Demonstr. Math., 39 (2006), 419–428.
[17]	L. B. Ćirić, J. S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Anal. Appl., 314 (2006), 488–499.
[18]	P. Debnath, M. de La Sen, Fixed-points of interpolative Ćirić-Reich-Rus-type contractions in b-metric spaces, Symmetry, 12 (2020), 12. https://doi.org/10.3390/sym12010012 doi: 10.3390/sym12010012
[19]	P. Debnath, M. de La Sen, Set-valued interpolative Hardy-Rogers and set-valued Reich-Rus-Ćirić-type contractions in b-metric spaces, Mathematics, 7 (2019). https://doi.org/10.3390/math7090849 doi: 10.3390/math7090849
[20]	P. Debnath, N. Konwar, S. Radenović, Metric fixed point theory: Applications in science, engineering and behavioural sciences, Springer Nature, Singapore, 2021. https://doi.org/10.1007/978-981-16-4896-0
[21]	P. Debnath, Z. D. Mitrović, S. Radenović, Interpolative Hardy-Rogers and Reich-Rus-Ćirić type contractions in b-metric and rectangular b-metric spaces, Mat. Vestn., 72 (2020), 368–374.
[22]	P. Hitzler, A. K. Seda, Dislocated topologies, J. Electr. Eng., 51 (2000), 3–7.
[23]	P. Hitzler, Generalized metrics and topology in logic programming semantics, PhD thesis, School of Mathematics, Applied Mathematics and Statistics, National University Ireland, University College Cork, 2001.
[24]	N. Hussain, J. R. Roshan, V. Paravench, M. Abbas, Common fixed point results for weak contractive mappings in ordered $b$-dislocated metric space with applications, J. Inequal. Appl., 2013 (2013), 1–21. https://doi.org/10.1186/1029-242X-2013-486 doi: 10.1186/1029-242X-2013-486
[25]	N. Hussain, J. R. Roshan, V. Paravench, A. Latif, A unification of $G$-metric, partial metric, and $b$-metric spaces, Abstr. Appl. Anal., 2014 (2014), 1–144. https://doi.org/10.1155/2014/180698 doi: 10.1155/2014/180698
[26]	A. Jeribi, B. Krichen, B. Mefteh, Existence solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations, J. Biol. Dynam., 7 (2013), 218–232.
[27]	E. Karapınar, O. Alqahtani, H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry, 11 (2019).
[28]	V. N. Mishra, L. M. Sánchez Ruiz, P. Gautam, S. Verma, Interpolative Reich-Rus-Ćirić and Hardy-Rogers contraction on quasi-partial $b$-metric space and related fixed point results, Mathematics, 8 (2020). https://doi.org/10.3390/sym11010008 doi: 10.3390/sym11010008
[29]	Z. Mustafa, V. Parvaneh, J. R. Roshan, Z. Kadelburg, $b_{2}$ -Metric spaces and some fixed point theorems, Fixed Point Theory A., 2014 (2014), 1–23. https://doi.org/10.1186/1687-1812-2014-144 doi: 10.1186/1687-1812-2014-144
[30]	Z. Mustafa, V. Parvaneh, M. Abbas, J. R. Roshan, Some coincidence point results for generalized ($\psi, \varphi $)-weakly contractive mappings in ordered $G$-metric spaces, Fixed Point Theory A., 2013 (2013). https://doi.org/10.1186/1687-1812-2013-326 doi: 10.1186/1687-1812-2013-326
[31]	Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces, J. Inequal Appl., 2013 (2013). https://doi.org/10.1186/1029-242X-2014-46 doi: 10.1186/1029-242X-2014-46
[32]	J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223–239. https://doi.org/10.1007/s11083-005-9018-5 doi: 10.1007/s11083-005-9018-5
[33]	M. Nazam, A. Mukheimer, H. Aydi, M. Arshad, R. Riaz, Fixed point results for dualistic contractions with an application, Discrete Dyn. Nat. Soc., 2020 (2020). https://doi.org/10.1155/2020/6428671 doi: 10.1155/2020/6428671
[34]	M. Nazam, H. Aydi, A. Hussain, Existence theorems for $\left(\Psi, \Phi \right) $-orthogonal interpolative contractions and an application to fractional differential equations, Optimization, 2022, 1–31. https://doi.org/10.1080/02331934.2022.2043858 doi: 10.1080/02331934.2022.2043858
[35]	A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443.
[36]	J. R. Roshan, N. Shobkolaei, S. Sedghi, V. Parvaneh, S. Radenović, Common fixed point theorems for three maps in discontinuous $G_{b}$- metric spaces, Acta Math. Sci., 34 (2014), 1643–1654.
[37]	A. Shoaib, I. S. Khan, Z. Hassan, Generalized contraction involving an open ball and common fixed point of multivalued mappings in ordered dislocated quasi metric spaces, Filomat, 34 (2020), 323–338. https://doi.org/10.2298/FIL2002323S doi: 10.2298/FIL2002323S
[38]	A. Shoaib, M. Arshad, T. Rasham, Some fixed point results in ordered complete dislocated quasi $G_{d}$ metric space, J. Comput. Anal. Appl., 29 (2021), 1036–1046.
[39]	A. Shoaib, Q. Mahmood, A. Shahzad, M. S. M. Noorani, S. Radenović, Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application, Adv. Differ. Equ., 2021 (2021), 1–15. https://doi.org/10.1186/s13662-021-03458-x doi: 10.1186/s13662-021-03458-x
[40]	J. Tiammee, S. Suantai, Fixed point theorems for monotone multi-valued mappings in partially ordered metric spaces, Fixed Point Theory A., 2014 (2014), 1–13. https://doi.org/10.1186/1687-1812-2014-110 doi: 10.1186/1687-1812-2014-110

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