Solving a nonlinear integral equation via orthogonal metric space

Arul Joseph Gnanaprakasam; Gunaseelan Mani; Jung Rye Lee; Choonkil Park; Arul Joseph Gnanaprakasam; Gunaseelan Mani; Jung Rye Lee; Choonkil Park

doi:10.3934/math.2022070

AIMS Mathematics

2022, Volume 7, Issue 1: 1198-1210. doi: 10.3934/math.2022070

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Research article

Solving a nonlinear integral equation via orthogonal metric space

1.
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram, Chennai, Tamil Nadu 603 203, India
2.
Department of Mathematics, Sri Sankara Arts and Science College (Autonomous), Affiliated to Madras University, Enathur, Kanchipuram, Tamil Nadu 631 561, India
3.
Department of Data Science, Daejin University, Kyunngi 11159, Korea
4.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 07 July 2021 Accepted: 11 October 2021 Published: 21 October 2021
MSC : 47H10, 54H25

We propose the concept of orthogonally triangular $ \alpha $-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.
- orthogonal set,
- orthogonal complete metric space,
- orthogonal continuous,
- orthogonal preserving,
- orthogonally triangular $ \alpha $-admissible,
- fixed point
Citation: Arul Joseph Gnanaprakasam, Gunaseelan Mani, Jung Rye Lee, Choonkil Park. Solving a nonlinear integral equation via orthogonal metric space[J]. AIMS Mathematics, 2022, 7(1): 1198-1210. doi: 10.3934/math.2022070

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Abstract

We propose the concept of orthogonally triangular $ \alpha $-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.

References

[1]	H. H. Alsulami, S. Gülyaz, E. Karapinar, I. M. Erhan, Fixed point theorems for a class of $\alpha$-admissible contractions and applications to boundary value problems, Abstr. Appl. Anal., 2014 (2014), 187031. doi: 10.1155/2014/187031. doi: 10.1155/2014/187031
[2]	I. Beg, M. Gunaseelan, G. Arul Joseph, Fixed point of orthogonal $F$-Suzuki contraction mapping on $O$-complete $b$-metric space with an application, J. Funct. Spaces, 2021 (2021), 6692112. doi: 10.1155/2021/6692112. doi: 10.1155/2021/6692112
[3]	M. Eshaghi Gordji, M. Ramezani, M. De la Sen, Y. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18 (2017), 569–578. doi: 10.24193/fpt-ro.2017.2.45. doi: 10.24193/fpt-ro.2017.2.45
[4]	M. Eshaghi Gordji, H. Habibi, Fixed point theory in generalized orthogonal metric space, J. Linear Topol. Algebra, 6 (2017), 251–260.
[5]	M. Eshaghi Gordji, H. Habibi, Fixed point theory in $\epsilon$-connected orthogonal metric space, Sahand Comm. Math. Anal., 16 (2019), 35–46. doi: 10.22130/scma.2018.72368.289. doi: 10.22130/scma.2018.72368.289
[6]	M. Gunaseelan, G. Arul Joseph, L. N. Mishra, V. N. Mishra, Fixed point theorem for orthogonal $F$-Suzuki contraction mapping on an $O$-complete metric space with an application, Malay. J. Mat., 1 (2021), 369–377. doi: 10.26637/MJM0901/0062. doi: 10.26637/MJM0901/0062
[7]	N. B. Gungor, D. Turkoglu, Fixed point theorems on orthogonal metric spaces via altering distance functions, AIP Conf. Proc., 2183 (2019), 040011. doi: 10.1063/1.5136131. doi: 10.1063/1.5136131
[8]	R. Maryam, Orthogonal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6 (2015), 127–132. doi: 10.22075/ijnaa.2015.261. doi: 10.22075/ijnaa.2015.261
[9]	M. S. Khan, S. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1–9. doi: 10.1017/S0004972700001659. doi: 10.1017/S0004972700001659
[10]	H. Piri, P. Kumam, Some fixed point theorems concerning $F$-contraction in complete metric spaces, Fixed Point Theory Appl., 2014 (2014), 210. doi: 10.1186/1687-1812-2014-210. doi: 10.1186/1687-1812-2014-210
[11]	K. Sawangsup, W. Sintunavarat, Fixed point results for orthogonal $Z$-contraction mappings in $O$-complete metric space, Int. J. Appl. Phys. Math., in press.
[12]	K. Sawangsup, W. Sintunavarat, Y. Cho, Fixed point theorems for orthogonal $F$-contraction mappings on $O$-complete metric spaces, J. Fixed Point Theory Appl., 22 (2020), 10. doi: 10.1007/s11784-019-0737-4. doi: 10.1007/s11784-019-0737-4
[13]	T. Senapati, L. K. Dey, B. Damjanović, A. Chanda, New fixed results in orthogonal metric spaces with an Application, Kragujevac J. Math., 42 (2018), 505–516.
[14]	F. Uddin, C. Park, K. Javed, M. Arshad, J. Lee, Orthogonal $m$-metric spaces and an application to solve integral equations, Adv. Differ. Equ., 2021 (2021), 159. doi: 10.1186/s13662-021-03323-x. doi: 10.1186/s13662-021-03323-x
[15]	D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 94. doi: 10.1186/1687-1812-2012-94. doi: 10.1186/1687-1812-2012-94
[16]	O. Yamaod, W. Sintunavarat, On new orthogonal contractions in $b$-metric spaces, Int. J. Pure Math., 5 (2018), 37–40.
[17]	Q. Yang, C. Bai, Fixed point theorem for orthogonal contraction of Hardy-Rogers-type mapping on $O$-complete metric spaces, AIMS Math., 5 (2020), 5734–5742. doi: 10.3934/math.2020368. doi: 10.3934/math.2020368

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