The phrase "a single or multivalued" is correct and usable in written English.
It can be used in contexts discussing data types, database fields, or programming concepts where values can either be singular or multiple.
Example: "In this database schema, the 'phone number' field can be defined as a single or multivalued attribute depending on the user's preference."
Alternatives: "one or multiple values" or "single value or multiple values".
The existence of fixed points for single or multivalued mappings is obtained as a corollary of Nash equilibrium existence in finitely many players games.
In [14] existence and uniqueness results are obtained for a single and multivalued case for the following boundary value problem of fractional order differential equations with nonlocal and fractional integral boundary conditions: D q u ( t ) = f ( t, u ( t ) ), 1 < q ≤ 2, t ∈ ( 0, 1 ), u ( 0 ) = u 0 + g ( u ), u ( 1 ) = α I α u , 0 < η < 1, (1.3).
Then the sequence { x n } converges weakly to x ¯ ∈ Ω. Proof Putting N = 1, then T i = T, a single multivalued nonexpansive mapping, and the conclusion follows immediately from Theorem 3.1.
Similar to the case of a single valued mapping, every multivalued nonexpansive mapping satisfies condition (C).
Let be a nonempty closed convex bounded subset of a uniformly convex Banach space,, and a single-valued and a multivalued nonexpansive mapping, respectively.
Much work has been done on the existence of common fixed points for a pair consisting of a single-valued and a multivalued mapping, see, for instance [7 14].
In this paper, we first present a common fixed point theorem for commuting pairs consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition.
Let be a nonempty compact convex subset of a uniformly convex Banach space, and let and be a single-valued and a multivalued nonexpansive mapping, respectively, and satisfying for all.
In 2011, Sokhuma and Kaewkhao [17] introduced a new iteration method for approximating a common fixed point of a pair of a single-valued and a multivalued nonexpansive mappings and proved the following strong convergence theorem: Theorem 1.2 ([17], Theorem 3.5]).
