A fixed point theorem for weak (𝛙 - 𝝋)-Jaggi type contraction
Abstract
In this paper, we introduce the weak (ψ − φ)-Jaggi type contraction. The existence and uniqueness of fixed point for such contraction is investigated. It is very helpful in extending the existing results of corresponding literature. In addition, we also provide an example in support of our theorem.
Downloads
References
Abbas M., Beg I., Coincidence point and invariant approximation for mapping satisfying generalized weak contractive condition, Fixed Point Theory and Applications, 2006, 1-7, (2006).
Alber Y.I., Guerre-Delabriere S., Principle of weakly contractive maps in Hilbert spaces, New results in Operator Theory and its Applications, 7-22, (1997).
Banach S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae 3, 133-181,(1922).
Boyd D. W., Wong J. S. W., On nonlinear contractions, Proc. Amer. Math. Soc. 20, 458-464,(1969).
Choudhury B.S., Das K., A new contraction principle in Menger spaces, Acta Mathematica Sinica, 8, 1379-1386, (2008).
Dutta P.N., Choudhury B.S., A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications, 2008, 1-8, (2008).
Jaggi D.S., Some unique fixed point theorems, Indian J. Pure Appl. Math., 2, 223-230, (1977).
Karapınar E, Fulga A., A hybrid contraction that involves Jaggi type, Symmetry, 5, 715, (2019).
Liouville J., Second mémoire sur le développement des fonctions ou parties de fonctions en séries dont divers termes sont assujettis á satisfaire a une m eme équation différentielle du second ordre contenant un paramétre variable, J. Math. Pure Appl., 2, 16–35, (1837).
Meir A., Keeler E., A theorem on contraction mappings, J. Math. Anal. Appl., 28, 326-329, (1969).
Picard E., Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives, J. Math. Pures Appl., 6, 145–210, (1890).
Rhoades B.E., Park S., Moon K.B., On generalizations of the Meir-Keeler type contraction maps, Journal of Mathematical Analysis and Applications, 14, 482-494, (1990).
Rhoades B.E., Some theorem on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications, 31, 71-81, (2001).
Zhang Q., Song Y., Fixed point theory for generalized ϕ-weak contractions, Applied Mathematics Letters, 1, 75-78, (2009).
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
