The phrase "a pair of generalized" is correct and usable in written English.
It can be used when referring to two generalized concepts, items, or categories in a specific context.
Example: "In our study, we examined a pair of generalized theories that explain the phenomenon."
Alternatives: "two generalized" or "a couple of generalized".
Also, by defining a pair of generalized stress intensity factors (SIFs) KI,β(t) and KII,β(t), the relationship between JkR t) and the SIF's is derived and expressed as functions of the notch angle β.
A class of reproducing kernel spaces with reproducing kernels of the form Kω = {J − ΘJΘ with pω = aa* is characterized in terms of invariance under a pair of generalized shift operators and a structural identity.
The purpose of this paper is to investigate a hybrid projection algorithm for a pair of generalized asymptotically quasi-ϕ-nonexpansive mappings.
In this paper, motivated by the above results, we investigate a hybrid projection algorithm for a pair of generalized asymptotically quasi-ϕ-nonexpansive mappings.
Here, ((overline{phi}_{1}(xi), overline{phi}_{2}(xi))), ((underline{phi}_{1}(xi), underline{phi}_{2}(xi))) are a pair of generalized upper and lower solutions of (2.1).
Vetro [8] introduced a notion of weak non-Archimedean fuzzy metric space and proved common fixed point results for a pair of generalized contractive-type mappings.
In this work, we introduce a generalized modified Krasnoselskii iterative process involving a pair of a generalized strictly pseudocontractive mapping and a generalized duality mapping and prove some strong convergence theorems of the proposed iterative process to the minimum norm solutions of certain nonlinear equations in the framework of uniformly convex Banach spaces.
In a recent paper [17] the authors obtained common fixed points of a pair of mapping satisfying generalized contractive type conditions without the assumption of normality in a class of topological vector space-valued cone metric spaces which is bigger than that of studied in [1 16].
Theorem 3.5 extends and generalizes the results of Sokhuma and Kaewkhao [11] to a pair of a finite family of generalized asymptotically nonexpansive single-valued mappings and a finite family of quasi-nonexpansive multi-valued mappings satisfying condition (E).
In this paper, motivated by the above results, we propose an iterative process for approximating a common fixed point of a pair of a finite family of generalized asymptotically nonexpansive single-valued mappings and a finite family of quasi-nonexpansive multi-valued mappings and prove weak and strong convergence theorems of the proposed iterative process in Banach spaces.
Theorems 3.5 and 3.7 extend and generalize the results of Eslamian [12] and Eslamian and Abkar [13] to a pair of a finite family of generalized asymptotically nonexpansive single-valued mappings and a finite family of quasi-nonexpansive multi-valued mappings satisfying condition (E).
