NEW FIXED POINT THEOREMS IN DISLOCATED METRIC SPACES

E. U. OFOEDU, C. S. ODILIOBI

Abstract


In this paper, the notion of dislocated metric space, which is a proper generalization of the notion of metric space is discussed. A new class of contractive mappings on dislocated metric space, called the class of 3 $\alpha$-contractive mappings is introduced. Using some classical results, new fixed point theorems are established in dislocated metric spaces for the class of 3$\alpha$-contractive mappings. Concrete examples and an application of our theorems to establishment of existence of solution
of certain two-point boundary value problem are given. As further findings of this research, certain anomalies detected in the existing literature are corrected.

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References


A. Amini-Harandi; Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl. (2012), 204.

A. H. Ansari and K. Zoto; Some fixed point theorems and cyclic contractions in dislocated quasi-metric spaces, Ser. Math. Inform., 33(1) (2018), 91-106.

H. Aydi and E. Karapinar; Fixed point results for generalized $alpha$ - $psi$ contractions in metric-like spaces and applications, Electronical Journal of Differential Equations, 2015(133) (2015), 1-15.

S. Beloul; A common fixed point theorems for generalized almost contractions n metric-like spaces, Applied Mathematics E-Notes, 18 (2018), 127-139.

R. George, R. Rajagopalan, H. A. Nabwey and S. Radenovic; Dislocated cone metric space over Banach algebra and $alpha$-quasi contraction mappings of Perov type, Fixed Point Theory and Applications, 2017:24, (2017),

DOI 10.1186/s13663-017-0619-7.

P. Hitzler; Generalized metrics and topologies in logic programming semantics, Phd thesis, School of Mathematics, Applied Mathematics and Statistics, National University of Ireland, University College Cork (2001).


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