Please use this identifier to cite or link to this item: https://scholar.ptuk.edu.ps/handle/123456789/139
Title: IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS
Authors: MARABEH IN, MOHAMMAD A. A.
Issue Date: May-2017
Publisher: MIDDLE EAST TECHNICAL UNIVERSITY
Citation: MIDDLE EAST TECHNICAL UNIVERSITY
Abstract: The main aim of this thesis is to generalize unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence to lattice-normed vector lattices (LNVLs). Therefore, we introduce the follwing notion: a net (x ) in an LNVL (X; p;E) is said to be unbounded p-convergent to x 2 X (shortly, x upconverges to x) if p(jx 􀀀 xj ^ u) o􀀀 ! 0 in E for all u 2 X+. Throughout this thesis, we study general properties of up-convergence. Besides, we introduce several notions in lattice-normed vector lattices which correspond to notions from vector and Banach lattice theory. Finally, we study briefly the mixed-normed spaces and use them for an investigation of up-null nets and up-null sequences in lattice-normed vector lattices. Keywords: Vector Lattice, Lattice-Normed Vector Lattice, up-Convergence, uo-Convergence, un-Convergence, uaw-Convergence, Mixed-Normed Space
URI: https://scholar.ptuk.edu.ps/handle/123456789/139
Appears in Collections:PH.D

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