Analysis for Quadrupled Fixed Point of Contractive-Type Multi-Valued Operators

Subject Areas : Operation Research

Samuel  Aniki ¹ (Department of Mathematics, Faculty of Science, Confluence University of Science and Technology, Osara, Kogi State, Nigeria)

Received: 2021-12-13 Accepted : 2022-04-16 Published : 2021-09-01

Keywords: Existence, Uniqueness, Data Dependence, Contractive-type, multi-valued,

Abstract :

This work considered the existence, uniqueness and data dependence of quadrupled fixed point theorems for contractions in metric spaces, equipped with vector-valued metrics whose approach is primarily based on Perov-type fixed point of contractive-type multi-valued mapping in Cauchy spaces. This work obtained results that complement recent and available results in literature.

References:

Aniki, S.A & Rauf, K. (2019). Stability results on coupled fixed point iterative procedures in complete metric spaces. Islamic University Multidisciplinary Journal 6(3), 175-186. ISSN 2617-6513.

Aniki, S.A. & Rauf, K. (2020). Stability theorem and results for quadrupled fixed point of contractive type single valued operators. Iranian Journal of Optimization, 12(2).

Berinde, V & Borcut, M. (2011). Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Analysis 74(15), 4889-4897.

Bhaskar, T.G & Lakshmikantham, V. (2006). Fixed point theory in partially ordered metric spaces and applications. Nonlinear Analysis 65, 1379-1393.

Cho, Y.J., Gupta, A., Karapinar, E & Kumam, P. (2013). Tripled best proximity point theorem in metric spaces. Mathematical Inequalities & Applications 16(4), 1197-1216.

Guo, D & Lakshmikantham, V. (1987). Coupled fixed points of nonlinear operators with applications. Nonlinear Analysis 11, 623-632.

Gupta, A. (2016). Ulam-Hyers stability theorem by tripled fixed point theorem. Fasciculi Mathematici, (56), 77-97.

Gupta, A. (2013). Weak contractions for coupled fixed point theorem on G-metric space, African Journal of Mathematics & Mathematical Science, 1(1), 1-12.

Gupta, A., Narayan, R & Yadava, R.N. (2014). Tripled fixed point for compatible mappings in partially ordered fuzzy metric spaces. The Journal of Fuzzy Mathematics 22(3), 565-580.

Lakshmikantham, V & Ciric, L. (2009). Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Analysis 70, 4341-4349.

Petru, P.T., Petrusel, A & Yao, J.C. (2011). Ulam-Hyers stability for operatorial equations and inclusions via nonself operators. Taiwanese Journal of Mathematics 15(5), 2195-2212.

Perov A.I. (1964). On the Cauchy problem for a system of ordinary differential equations, Pviblizhen Metody Reshen Differential Uvavn 2, 115-134.

Rauf, K & Aniki, S.A. (2021). Quadrupled fixed point theorems for contractive type mappings in partially ordered cauchy spaces. Confluence Journal of Pure and Applied Sciences. 4(1), 18-30.

Rus, M.D. (2009). Remarks on Ulam stability of the operatorial equations. Fixed Point Theory 10(2), 305-320.