Abstract
AbstractEvery non-convex pair $(C, D)$
(
C
,
D
)
may not have proximal normal structure even in a Hilbert space. In this article, we use cyclic relatively nonexpansive maps with respect to orbits to show the presence of best proximity points in $C\cup D$
C
∪
D
, where $C\cup D$
C
∪
D
is a cyclic T-regular set and $(C, D)$
(
C
,
D
)
is a non-empty, non-convex proximal pair in a real Hilbert space. Moreover, we show the presence of best proximity points and fixed points for non-cyclic relatively nonexpansive maps with respect to orbits defined on $C\cup D$
C
∪
D
, where C and D are T-regular sets in a uniformly convex Banach space satisfying $T(C)\subseteq C$
T
(
C
)
⊆
C
, $T(D)\subseteq D$
T
(
D
)
⊆
D
wherein the convergence of Kranoselskii’s iteration process is also discussed.
Funder
University Grants Commission
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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