Sentence examples for regular with respect from inspiring English sources

Let be a bounded sequence in which is regular with respect to.

Then ({x_{n}}) has a subsequence that is regular with respect to C.

Since B is uniformly asymptotically regular with respect to A, it follows that (3.21).

For (n=1) this equivalent to (Omega ) being regular with respect to classical potential theory.

(i) (See Goebel [26] and Lim [27]) There always exists a subsequence of which is regular with respect to.

A bounded sequence is said to be regular with respect to if for every subsequence we have (3.5).

Hence the sequence { x n } is asymptotically T-regular with respect to f.

Since X is α-regular with respect to g and (2.19), we have alpha(gx_{n k)+1},gx geq1 quad mbox{for all }k in mathbb{N}.

Therefore it is convergent to the infimum, that is, d ( f x n, T x n ) → inf { d ( f x n, T x n ) : n ∈ N } = 0, and { x n } is asymptotically T-regular with respect to f in Y. □.

T is g-α-admissible and triangular α-admissible; there exists (x_{0}in X) such that (alpha (gx_{0},Tx_{0} geq1); X is α-regular with respect to g.

Assume that the mapping T is an almost generalized ((alphamboxpsimboxvarphimboxtheta ))-contractive mapping with respect to g and the following conditions hold: (i) T is g-α-admissible and triangular α-admissible;   (ii) there exists (x_{0}in X) such that (alpha (gx_{0},Tx_{0} geq1);   (iii) X is α-regular with respect to g.   Then T and g have a coincidence point.