Solving an integral equation via orthogonal generalized $ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}}  $-Geraghty contractions

Senthil Kumar Prakasam; Arul Joseph Gnanaprakasam; Gunaseelan Mani; Fahd Jarad; Senthil Kumar Prakasam; Arul Joseph Gnanaprakasam; Gunaseelan Mani; Fahd Jarad

doi:10.3934/math.2023297

AIMS Mathematics

2023, Volume 8, Issue 3: 5899-5917. doi: 10.3934/math.2023297

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Solving an integral equation via orthogonal generalized $ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractions

1.
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, Tamil Nadu, India
2.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India
3.
Department of Mathematics, Çankaya University, Etimesgut 06790, Ankara, Turkey
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 13 October 2022 Revised: 11 December 2022 Accepted: 19 December 2022 Published: 27 December 2022
MSC : 47H10, 54H25

In this paper, we introduce orthogonal generalized $ {\bf{O}} $-$ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractive type mappings and prove some fixed point theorems in $ {\bf{O}} $-complete $ {\bf{O}} $-$ \mathfrak{b} $-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application.
Citation: Senthil Kumar Prakasam, Arul Joseph Gnanaprakasam, Gunaseelan Mani, Fahd Jarad. Solving an integral equation via orthogonal generalized $ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractions[J]. AIMS Mathematics, 2023, 8(3): 5899-5917. doi: 10.3934/math.2023297

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Abstract

In this paper, we introduce orthogonal generalized $ {\bf{O}} $-$ {\boldsymbol{\alpha}} $-$ {\boldsymbol{\psi}} $-Geraghty contractive type mappings and prove some fixed point theorems in $ {\bf{O}} $-complete $ {\bf{O}} $-$ \mathfrak{b} $-metric spaces. We also provide an illustrative example to support our theorem. The results proved here will be utilized to show the existence of a solution to an integral equation as an application.

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