Abstract
In this article, we introduce a new type of generalized multivalued Hardy and Roger’s type proximal contractive and proximal cyclic contractive mappings of b -metric spaces and develop some results for the existence of best proximity point(s). Moreover, we obtain some results for the existence and uniqueness of best proximity points for single-valued mappings. Examples are given to explain the main results.
Highlights
A mapping that satisfies (1) is known as Banach contraction
Many mathematicians contributed for the development of fixed-point theory by producing many results with different generalized contractive mappings in complete metric spaces, for details one can see [2,3,4,5,6,7,8] and the references therein
The metric space has been generalized to b-metric space; the fixed point theory has been further generalized for single-valued and multivalued mappings in the context of b-metric space, for instance, Bakhtin [15] in 1989 and Czerwik [16] in 1993
Summary
A mapping that satisfies (1) is known as Banach contraction. After this remarkable result, many mathematicians contributed for the development of fixed-point theory by producing many results with different generalized contractive mappings in complete metric spaces, for details one can see [2,3,4,5,6,7,8] and the references therein. A mapping T: R ⟶ ℘(S) is said to be a new type of generalized multivalued Hardy and Roger’s proximal contractive mapping if ρb r1, Tr3 ρb(R, S) ⎫⎪⎪⎪⎪⎬ ρb r2, Tr4 ρb(R, S) ⎪⎪⎪⎪⎭, r3 ≠ r4 implies, ρb r1, r2 < αρb r1, r3 + βρb c r2, r4 + b2ρb r3, r4 ⎫⎪⎪⎪⎪⎪⎬
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
