Existence of $ \varphi $-fixed point for generalized contractive mappings

Maryam Shams; Sara Zamani; Shahnaz Jafari; Manuel De La Sen; Maryam Shams; Sara Zamani; Shahnaz Jafari; Manuel De La Sen

doi:10.3934/math.2021411

AIMS Mathematics

2021, Volume 6, Issue 7: 7017-7033. doi: 10.3934/math.2021411

Previous Article Next Article

Research article

Existence of $ \varphi $-fixed point for generalized contractive mappings

1.
Department of Mathematics, shahrekord university, Iran
2.
Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, Spain

Received: 25 December 2020 Accepted: 19 April 2021 Published: 26 April 2021
MSC : 47H09, 47H10

In this paper, we first define the generalized (F, $ \varphi $, $ \alpha - \psi $)-contraction mappings. In the following, we consider the conditions in which these mappings have a $ \varphi $-fixed point and also we present examples and applications of these mappings in partial metric space and integral equations.
Citation: Maryam Shams, Sara Zamani, Shahnaz Jafari, Manuel De La Sen. Existence of $ \varphi $-fixed point for generalized contractive mappings[J]. AIMS Mathematics, 2021, 6(7): 7017-7033. doi: 10.3934/math.2021411

Related Papers:

Abstract

In this paper, we first define the generalized (F, $ \varphi $, $ \alpha - \psi $)-contraction mappings. In the following, we consider the conditions in which these mappings have a $ \varphi $-fixed point and also we present examples and applications of these mappings in partial metric space and integral equations.

References

[1]	S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181. doi: 10.4064/fm-3-1-133-181
[2]	B. Samet, C. Vetro, P. Vetro, Fixed point theorems for $ \alpha-\psi $-contractive type mappings, Nonlinear Analy.: Theor., 75 (2012), 2154–2165. doi: 10.1016/j.na.2011.10.014
[3]	H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topol. Appl., 159 (2012), 3234–3242. doi: 10.1016/j.topol.2012.06.012
[4]	M. S. Adamo, C. Vetro, Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces, Nonlinear Anal.: Model., 20 (2015), 159–174. doi: 10.15388/NA.2015.2.1
[5]	H. Aydi, M. Jellali, E. Karapınar, On fixed point results for alpha-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal.: Model., 21 (2016), 40–56.
[6]	M. Jleli, B. Samet, C. Vetro, Fixed point theory in partial metric spaces via $ \varphi $-fixed point's concept in metric spaces, J. Inequal. Appl., 2014 (2014), 1–9. doi: 10.1186/1029-242X-2014-1
[7]	M. Asadi, Discontinuity of control function in the $ (F, \varphi, \theta) $-contraction in metric spaces, Filomat, 31 (2017), 5427–5433. doi: 10.2298/FIL1717427A
[8]	E. Karapinar, D. O'Regan, B. Samet, On the existence of fixed points that belong to the zero set of a certain function, Fixed Point Theory Appl., 2015 (2015), 1–14. doi: 10.1186/1687-1812-2015-1
[9]	M. Imdad, A. R. Khan, H. N. Saleh, W. M. Alfaqih, Some $ \varphi $-fixed point results for $ (F, \varphi, \alpha-\psi)$-contractive type mappings with applications, Mathematics, 7 (2019), 122. doi: 10.3390/math7020122
[10]	S. G. Matthews, Partial metric topology, Ann. NY. Acad. Sci., 728 (1994), 183–197.
[11]	X. Ge, S. Lin, Completions of partial metric spaces, Topol. Appl., 182 (2015), 16–23. doi: 10.1016/j.topol.2014.12.013
[12]	X. Ge, S. Lin, Contractions of Nadler type on partial tvs-cone metric spaces, Colloq. Math-Warsaw, 138 (2015), 149–163. doi: 10.4064/cm138-2-1
[13]	X. Ge, S. Yang, Some fixed point results on generalized metric spaces, AIMS Mathematics, 6 (2021), 1769–1780. doi: 10.3934/Math.2021106

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)