Fixed Point Theorem for Single valued Mapping in Convex Partial Symmetric Spaces with an Application

Year 2022, Volume: 10 Issue: 2, 332 - 340, 31.10.2022

Lucas Wangwe Santosh Kumar

Abstract

In this paper, we proved a fixed point theorem for single-valued mapping in convex partial symmetric spaces. In doing so, we extended and generalised the theorem due to Asim et al. [3] by employing a convex structure for single-valued Kannan type contractions. We also provided an illustrative example to support the results and an
application to integral equation.

Keywords

Fixed point, partial symmetric spaces,, convex partial symmetric spaces,, single-valued mapping, integral equation.

Supporting Institution

None

Project Number

NIL

Thanks

None

References

• [1] Agarwal, R. P., O'Regan, D., Sahu, D. R., Fixed Point Theory for Lipschitzian-Type Mappings with Applications, Springer, Heidelberg (2009), 2009.
• [2] Asadi, M., Some results of fixed point theorems in convex metric spaces, Nonlinear Funct. Anal. Appl, 19(2)(2014), 171-175.
• [3] Asim, M., Khan, A. R., Imdad, M., Fixed point results in Partial Symmetric spaces with an application, Axioms (MDPI), 8(1)(2019), 1-15.
• [4] Beg, I., Abbas, M., Common fixed points and best approximation in convex metric spaces, Soochow Journal of Mathematics, 33(4)(2007), 729-738.
• [5] Cho, S., Bae, J., Common fixed point theorems for mappings satisfying property (E.A.) on cone metric spaces, Mathematical and Computer Modelling, 53(5-6)(2011), 945-951.
• [6] Hunter, J. K., Nachtergaele, B., Applied Analysis, River Edge, NJ: World Scientific Publishing, Co., Inc.; 2001.
• [7] Imdad, M., Javid, A., Common fixed point theorems in symmetric spaces employing a new implicit function and common property (E.A.), The Belgian Mathematical Society. Bulletin of the Belgian Mathematical Society-Simon Stevin, 16(3)(2000), 421-433.
• [8] Karapinar, E., Fixed point theorems in cone Banach spaces, Fixed Point Theory and Applications, 2009, Article ID609281(2009). doi:10.1155/2009/609281
• [9] Matthews, S., Partial metric topology in Papers on General Topology and Applications, Eighth Summer Conference at Queens College, Eds. S. Andima et al., Annals of the New York Academy of Sciences, Vol. 728(1994), 183-197.
• [10] Moosaei, M., Fixed point theorems in convex metric spaces, Springer, Fixed Point Theory and Applications, 2012(1)(2012), 1-6.
• [11] Nazam, M., Arshad, M., Aftab, H., On Convex Structures in Pseudo Metric Spaces and Fixed Point Theorems, Publ. j.Ana. Num. Ther, 5(1)(2017), 57-62.
• [12] Oussaeif, T., Fixed point theorems in convex partial metric spaces, Konuralp Journal of Mathematics, 2(2)(2014), 96-101.
• [13] Takahashi, T., A convexity in metric spaces and non-expansive mapping, Kodai Math. Sem. Rep., 22(2) (1970), 142-149.