Sentence examples for generalized convergence from inspiring English sources

The purpose of this paper is to extend a generalized convergence method, namely, statistical convergence to sequences of fuzzy numbers of multiplicity greater than two.

Using lacunary sequences, Fridy et al.[7] defined S θ -convergence, a generalized statistical convergence as follows.

In [37], Hazarika introduced the generalized statistical convergence in random 2-normed spaces.

In this paper, we establish several generalized complete convergence results for pairwise negatively quadrant dependent random sequences, which include some well-known results.

Motivated by the above works, the main purposes of the paper are to give several generalized complete convergence results for pairwise NQD random sequences, which include some well-known results.

Hazarika [32] gave the definition of lacunary generalized difference statistical convergence in random 2-normed spaces.

By generalized statistical τ-convergence to ξ, there is p ∈ N with ξ − x p ∈ E and lim n → ∞ 1 λ n | { j ∈ I n : x j − ξ ∉ E } | = 0. Also, for all n ∈ N and j ∈ ( N ∖ K ) ∩ I n, where K = { j ∈ N : x j − ξ ∉ E }, we have x j − x p = x j − ξ + ξ − x p ∈ E + E ⊆ Y ⊆ U. and δ λ ( K ) = 0. Therefore the set { j ∈ N : x j − x p ∉ U } ⊆ K ∩ I n. for all n ∈ N.

Further, they also proved the existence of solutions for nonlinear variational inclusions involving generalized -accretive mappings and convergence of sequences generated by the algorithms.

This paper aims to study the strong convergence of generalized modified Krasnoselskii iterative process for finding the minimum norm solutions of certain nonlinear equations with generalized strictly pseudocontractive, demiclosed, coercive, bounded, and potential mappings in uniformly convex Banach spaces.

We generate a strong convergence theorem for the sequence considered by the generalized method.

We prove the generalized stability and the convergence of the scheme.