Fixed point for an $ \mathbb{O}g\mathfrak{F} $-c in $ \mathbb{O} $-complete $ \mathfrak{b} $-metric-like spaces

Senthil Kumar Prakasam; Arul Joseph Gnanaprakasam; Ozgur Ege; Gunaseelan Mani; Salma Haque; Nabil Mlaiki; Senthil Kumar Prakasam; Arul Joseph Gnanaprakasam; Ozgur Ege; Gunaseelan Mani; Salma Haque; Nabil Mlaiki

doi:10.3934/math.2023050

AIMS Mathematics

2023, Volume 8, Issue 1: 1022-1039. doi: 10.3934/math.2023050

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Fixed point for an $ \mathbb{O}g\mathfrak{F} $-c in $ \mathbb{O} $-complete $ \mathfrak{b} $-metric-like spaces

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, Faculty of Science, Ege University, Bornova, 35100, Izmir, Turkey
3.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 22 July 2022 Revised: 04 September 2022 Accepted: 26 September 2022 Published: 14 October 2022
MSC : 47H10, 54H25

In this article, we present the concepts of $ \mathbb{O} $-generalized $ \mathfrak{F} $-contraction of type-$ (1) $, type-$ (2) $ and prove several fixed point theorems for a self mapping in $ \mathfrak{b} $- metric-like space. The proved results generalize and extend some of the well known results in the literature. An example to support our result is presented. As an application of our results, we demonstrate the existence of a unique solution to an integral equation.
Citation: Senthil Kumar Prakasam, Arul Joseph Gnanaprakasam, Ozgur Ege, Gunaseelan Mani, Salma Haque, Nabil Mlaiki. Fixed point for an $ \mathbb{O}g\mathfrak{F} $-c in $ \mathbb{O} $-complete $ \mathfrak{b} $-metric-like spaces[J]. AIMS Mathematics, 2023, 8(1): 1022-1039. doi: 10.3934/math.2023050

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Abstract

In this article, we present the concepts of $ \mathbb{O} $-generalized $ \mathfrak{F} $-contraction of type-$ (1) $, type-$ (2) $ and prove several fixed point theorems for a self mapping in $ \mathfrak{b} $- metric-like space. The proved results generalize and extend some of the well known results in the literature. An example to support our result is presented. As an application of our results, we demonstrate the existence of a unique solution to an integral equation.

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