On elliptic valued b-metric spaces and some new fixed point results with an application

Sudipta Kumar Ghosh; Ozgur Ege; Junaid Ahmad; Ahmad Aloqaily; Nabil Mlaiki; Sudipta Kumar Ghosh; Ozgur Ege; Junaid Ahmad; Ahmad Aloqaily; Nabil Mlaiki

doi:10.3934/math.2024835

AIMS Mathematics

2024, Volume 9, Issue 7: 17184-17204. doi: 10.3934/math.2024835

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Research article

On elliptic valued b-metric spaces and some new fixed point results with an application

1.
Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar 751024, Odisha, India
2.
Department of Mathematics, Faculty of Science, Ege University, Bornova, 35100 Izmir, Turkey
3.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
5.
School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia

Received: 10 March 2024 Revised: 19 April 2024 Accepted: 24 April 2024 Published: 17 May 2024
MSC : 47H09, 47H10, 54H25

In this paper, we introduce the concept of elliptic-valued b-metric spaces, extending the notions of elliptic-valued metric spaces and complex-valued metric spaces. We present several fixed-point results that involve rational and product terms within this novel space framework. To support our main findings, we offer numerical examples. Additionally, we demonstrate an application of Urysohn integral equations.
- $ \alpha $-admissible mapping,
- rational product terms,
- elliptic-valued b-metric space,
- simulation function,
- Caristi-type fixed point,
- Urysohn integral equation
Citation: Sudipta Kumar Ghosh, Ozgur Ege, Junaid Ahmad, Ahmad Aloqaily, Nabil Mlaiki. On elliptic valued b-metric spaces and some new fixed point results with an application[J]. AIMS Mathematics, 2024, 9(7): 17184-17204. doi: 10.3934/math.2024835

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Abstract

In this paper, we introduce the concept of elliptic-valued b-metric spaces, extending the notions of elliptic-valued metric spaces and complex-valued metric spaces. We present several fixed-point results that involve rational and product terms within this novel space framework. To support our main findings, we offer numerical examples. Additionally, we demonstrate an application of Urysohn integral equations.

References

[1]	S. G. Georgiev, K. Zennir, Classical solutions for a class of IVP for nonlinear two-dimensional wave equations via new fixed point approach, Partial Differential Equations in Applied Mathematics, 2 (2020), 100014. https://doi.org/10.1016/j.padiff.2020.100014 doi: 10.1016/j.padiff.2020.100014
[2]	S. G. Georgiev, K. Zennir, Multiple fixed-point theorems and applications in the theory of ODEs, FDEs and PDEs, New York: Chapman and Hall/CRC, 2020. https://doi.org/10.1201/9781003028727
[3]	A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Func. Anal. Opt., 32 (2011), 243–253. https://doi.org/10.1080/01630563.2011.533046 doi: 10.1080/01630563.2011.533046
[4]	W. Shatanawi, T. A. M. Shatnawi, New fixed point results in controlled metric type spaces based 213 on new contractive conditions, AIMS Mathematics, 8 (2023), 9314–9330. https://doi.org/10.3934/math.2023468 doi: 10.3934/math.2023468
[5]	M. Joshi, A. Tomar, T. Abdeljawad, On fixed points, their geometry and application to satellite web coupling problem in S-metric spaces, AIMS Mathematics, 8 (2023), 4407–4441. https://doi.org/10.3934/math.2023220 doi: 10.3934/math.2023220
[6]	A. Z. Rezazgui, A. A. Tallafha, W. Shatanawi, Common fixed point results via Aν-$\alpha$-contractions with a pair and two pairs of self-mappings in the frame of an extended 216 quasi b-metric space, AIMS Mathematics, 8 (2023), 7225–7241. https://doi.org/10.3934/math.2023363 doi: 10.3934/math.2023363
[7]	A. A. Mukheimer, Some common fixed point theorems in complex valued b-metric spaces, Sci. World J., 2014 (2014), 587825. https://doi.org/10.1155/2014/587825 doi: 10.1155/2014/587825
[8]	W. Sintunavarat, Y. J. Cho, P. Kumam, Urysohn integral equations approach by common fixed points in complex-valued metric spaces, Adv. Differ. Equ., 2013 (2013), 49. https://doi.org/10.1186/1687-1847-2013-49 doi: 10.1186/1687-1847-2013-49
[9]	K. Sitthikul, S. Saejung, Some fixed point theorems in complex valued metric spaces, Fixed Point Theory Appl., 2012 (2012), 189. https://doi.org/10.1186/1687-1812-2012-189 doi: 10.1186/1687-1812-2012-189
[10]	R. K. Verma, H. K. Pathak, Common fixed point theorems using property (E.A) in complex-valued metric spaces, Thai J. Math., 11 (2013), 347–355.
[11]	M. Öztürk, I. A. Kösal, H. H. Kösal, Coincidence and common fixed point theorems via $\varrho$-class functions in elliptic valued metric spaces, An. Sti. U. Ovid. Con. Mat., 29 (2021), 165–182. https://doi.org/10.2478/auom-2021-0011 doi: 10.2478/auom-2021-0011
[12]	L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476. https://doi.org/10.1016/j.jmaa.2005.03.087 doi: 10.1016/j.jmaa.2005.03.087
[13]	I. A. Bakhtin, The contraction mapping principle in almost metric spaces, J. Funct. Anal., 30 (1989), 26–37.
[14]	S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostrav., 1 (1993), 5–11.
[15]	M. Demma, R. Saadati, P. Vetro, Fixed point results on b-metric space via Picard sequences and b-simulation functions, Iran. J. Math. Sci. Info., 11 (2016), 123–136. https://doi.org/10.7508/ijmsi.2016.01.011 doi: 10.7508/ijmsi.2016.01.011
[16]	X. L. Liu, A. H. Ansari, S. Chandok, S. N. Radenovic, On some results in metric spaces using auxiliary simulation functions via new functions, J. Comput. Anal. Appl., 24 (2018), 1103–1114.
[17]	R. Miculescu, A. Mihail, New fixed point theorems for set-valued contractions in b-metric spaces, J. Fixed Point Theory Appl., 19 (2017), 2153–2163. https://doi.org/10.1007/s11784-016-0400-2 doi: 10.1007/s11784-016-0400-2
[18]	O. Popescu, Some new fixed point theorems for $\alpha$-Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 190. https://doi.org/10.1186/1687-1812-2014-190 doi: 10.1186/1687-1812-2014-190
[19]	E. Karapınar, V. M. L. H. Bindu, Discussions on the almost $\mathcal{Z}$-contraction, Open Math., 18 (2020), 448–457. https://doi.org/10.1515/math-2020-0174 doi: 10.1515/math-2020-0174
[20]	J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), 241–251. https://doi.org/10.1090/S0002-9947-1976-0394329-4 doi: 10.1090/S0002-9947-1976-0394329-4
[21]	A. Fulga, On interpolative contractions that involve rational forms, Adv. Differ. Equ., 2021 (2021), 448. https://doi.org/10.1186/s13662-021-03605-4 doi: 10.1186/s13662-021-03605-4

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