Sentence examples for mappings without any from inspiring English sources

In addition, they also established an existence theorem for fixed points of ((alpha,psi -Meir-Keeler-Khan malpha,psi -Meir-Keeler-Khanty alpha,psi -Meir-Keeler-Khan8].

Theorem 3.1 is an improved probabilistic version of the result of Sedghi et al. [[55], Theorem 1] for two pairs of mappings without any requirement on containment of ranges amongst the involved mappings.

Theorem 3.3 extends the main result of Ciric [30] to Menger PM spaces besides extending the main result of Kubiaczyk and Sharma [20] to two pairs of mappings without any condition on containment of ranges amongst involved mappings.

We prove, under certain appropriate assumptions on the sequences and, that defined by (1.6) converges to a common fixed point of the finite family nonexpansive mappings without any commutative assumptions.

The mappings are further classified into three classes: all mappings without any mismatches belong to the Perfect Match class.

Recently, Imdad et al. [33] extended the notion of common limit range property to two pairs of self-mappings without any requirement on closedness of the underlying subspaces.

Remark 3.2 Theorem 3.1 is an improved probabilistic version of the result of Sedghi et al. [[55], Theorem 1] for two pairs of self-mappings without any requirement on containment of ranges amongst the involved mappings.

Our next result is an existence theorem on common attractive points of two further generalized hybrid mappings (1.3) without any use of closedness and convexity.

Motivated by this, we prove a common fixed point theorem for a pair of fuzzy mappings without taking into account any commutativity condition in complete ordered metric spaces.

The aim of this paper is to obtain the common end point, a special case of fixed point, of two multivlaued mappings without appeal to continuity of any map involved therein.

Is there any strong convergence theorem of Moudafi's type for quasi-nonexpansive mappings without using the demiclosedness principle in a Banach space E?