On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with 𝑝-Orthogonal Summands. Correction

2003 ◽  
Vol 10 (4) ◽  
pp. 799-802
Author(s):  
Andrew Rosalsky ◽  
Andrei I. Volodin
Keyword(s):  
Acta Math ◽  
Convergence Of Series ◽  
Corrected Version ◽  
Random Elements ◽  
Maximal Moment ◽  
Martingale Convergence

Abstract A result by Móricz, Su, and Taylor from Acta Math. Hungar. 65(1994), 1–16, was misstated in the authors' paper in Georgian Math. J. 8(2001), No. 2, 377–388, where due to this misstatement the invalid formulation and proof of a corollary is given. In this correction note, the needed result is correctly stated and a corrected version of the invalid corollary is proved.

On Convergence of Series of Random Elements via Maximal Moment Relations with Applications to Martingale Convergence and to Convergence of Series with p-Orthogonal Summands

2001 ◽  
Vol 8 (2) ◽  
pp. 377-388
Author(s):  
Andrew Rosalsky ◽  
Andrei I. Volodin
Keyword(s):  
Banach Space ◽  
Convergent Series ◽  
Difference Sequence ◽  
Martingale Difference ◽  
Nonlinear Anal ◽  
Convergence Of Series ◽  
Special Cases ◽  
Random Elements ◽  
Maximal Moment ◽  
Martingale Convergence

Abstract The rate of convergence for an almost surely convergent series of Banach space valued random elements is studied in this paper. As special cases of the main result, known results are obtained for a sequence of independent random elements in a Rademacher type p Banach space, and new results are obtained for a martingale difference sequence of random elements in a martingale type p Banach space and for a p-orthogonal sequence of random elements in a Rademacher type p Banach space. The current work generalizes, simplifies, and unifies some of the recent results of Nam and Rosalsky [Teor. Īmovīr. ta Mat. Statist. 52: 120–131, 1995] and Rosalsky and Rosenblatt [Bull. Inst. Math. Acad. Sinica 11: 185–208, 1983, Nonlinear Anal. 30: 4237–4248, 1997].

On convergence of series of independent random elements in banach spaces

1999 ◽  
Vol 17 (1) ◽  
pp. 85-97 ◽  
Author(s):  
Eunwoo Nam ◽  
Andrew Rosalsky ◽  
Andrej I. Volodin
Keyword(s):  
Banach Spaces ◽  
Convergence Of Series ◽  
Random Elements

On the rate of convergence of series of banach space valued random elements

Nonlinear Analysis ◽  
1997 ◽  
Vol 30 (7) ◽  
pp. 4237-4248 ◽  
Author(s):  
Andrew Rosalsky ◽  
Joseph Rosenblatt
Keyword(s):  
Banach Space ◽  
Rate Of Convergence ◽  
Convergence Of Series ◽  
Random Elements

Coincidence and fixed points for hybrid tangential maps

2010 ◽  
Vol 17 (2) ◽  
pp. 273-285
Author(s):  
Tayyab Kamran ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Property ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contractive Condition ◽  
The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

scholarly journals The Calderón–Zygmund Theorem with an $$L^1$$ Mean Hörmander Condition

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Soichiro Suzuki
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Acta Math ◽  
Limited Range ◽  
Singular Integral Operators ◽  
Convolution Type ◽  
Worst Case ◽  
Hörmander Condition

AbstractIn 2019, Grafakos and Stockdale introduced an $$L^q$$ L q mean Hörmander condition and proved a “limited-range” Calderón–Zygmund theorem. Comparing their theorem with the classical one, it requires weaker assumptions and implies the $$L^p$$ L p boundedness for the “limited-range” instead of $$1< p < \infty $$ 1 < p < ∞ . However, in this paper, we show that the $$L^q$$ L q mean Hörmander condition is actually enough to obtain the $$L^p$$ L p boundedness for all $$1< p < \infty $$ 1 < p < ∞ even in the worst case $$q=1$$ q = 1 . We use a similar method to that used by Fefferman (Acta Math 124:9–36, 1970): form the Calderón–Zygmund decomposition with the bounded overlap property and approximate the bad part. Also we give a criterion of the $$L^2$$ L 2 boundedness for convolution type singular integral operators under the $$L^1$$ L 1 mean Hörmander condition.

scholarly journals Certain fundamental properties of generalized natural transform in generalized spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Khalaf Al-Omari ◽  
Serkan Araci
Keyword(s):  
Inversion Formula ◽  
Acta Math ◽  
Generalized Functions ◽  
General Nature ◽  
Qualitative Behavior ◽  
Fundamental Properties ◽  
Integrable Functions ◽  
Extended Operator ◽  
Definition Of ◽  
Space Of Integrable Functions

AbstractThis paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

scholarly journals Ideal simplices and double-simplices, their non-orientable hyperbolic manifolds, cone manifolds and orbifolds with Dehn type surgeries and graphic analysis

2021 ◽  
Vol 112 (1) ◽  
Author(s):  
E. Molnár ◽  
I. Prok ◽  
J. Szirmai
Keyword(s):  
Acta Math ◽  
Hyperbolic Manifolds ◽  
Space Forms ◽  
Hyperbolic Structures ◽  
Princeton University ◽  
Regular Ideal ◽  
Graphic Analysis ◽  
Novi Sad ◽  
Memorial Volume ◽  
János Bolyai

AbstractIn connection with our works in Molnár (On isometries of space forms. Colloquia Math Soc János Bolyai 56 (1989). Differential geometry and its applications, Eger (Hungary), North-Holland Co., Amsterdam, 1992), Molnár (Acta Math Hung 59(1–2):175–216, 1992), Molnár (Beiträge zur Algebra und Geometrie 38/2:261–288, 1997) and Molnár et al. (in: Prékopa, Molnár (eds) Non-Euclidean geometries, János Bolyai memorial volume mathematics and its applications, Springer, Berlin, 2006), Molnár et al. (Symmetry Cult Sci 22(3–4):435–459, 2011) our computer program (Prok in Period Polytech Ser Mech Eng 36(3–4):299–316, 1992) found 5079 equivariance classes for combinatorial face pairings of the double-simplex. From this list we have chosen those 7 classes which can form charts for hyperbolic manifolds by double-simplices with ideal vertices. In such a way we have obtained the orientable manifold of Thurston (The geometry and topology of 3-manifolds (Lecture notes), Princeton University, Princeton, 1978), that of Fomenko–Matveev–Weeks (Fomenko and Matveev in Uspehi Mat Nauk 43:5–22, 1988; Weeks in Hyperbolic structures on three-manifolds. Ph.D. dissertation, Princeton, 1985) and a nonorientable manifold $$M_{c^2}$$ M c 2 with double simplex $${\widetilde{{\mathcal {D}}}}_1$$ D ~ 1 , seemingly known by Adams (J Lond Math Soc (2) 38:555–565, 1988), Adams and Sherman (Discret Comput Geom 6:135–153, 1991), Francis (Three-manifolds obtainable from two and three tetrahedra. Master Thesis, William College, 1987) as a 2-cusped one. This last one is represented for us in 5 non-equivariant double-simplex pairings. In this paper we are going to determine the possible Dehn type surgeries of $$M_{c^2}={\widetilde{{\mathcal {D}}}}_1$$ M c 2 = D ~ 1 , leading to compact hyperbolic cone manifolds and multiple tilings, especially orbifolds (simple tilings) with new fundamental domain to $${\widetilde{{\mathcal {D}}}}_1$$ D ~ 1 . Except the starting regular ideal double simplex, we do not get further surgery manifold. We compute volumes for starting examples and limit cases by Lobachevsky method. Our procedure will be illustrated by surgeries of the simpler analogue, the Gieseking manifold (1912) on the base of our previous work (Molnár et al. in Publ Math Debr, 2020), leading to new compact cone manifolds and orbifolds as well. Our new graphic analysis and tables inform you about more details. This paper is partly a survey discussing as new results on Gieseking manifold and on $$M_{c^2}$$ M c 2 as well, their cone manifolds and orbifolds which were partly published in Molnár et al. (Novi Sad J Math 29(3):187–197, 1999) and Molnár et al. (in: Karáné, Sachs, Schipp (eds) Proceedings of “Internationale Tagung über geometrie, algebra und analysis”, Strommer Gyula Nemzeti Emlékkonferencia, Balatonfüred-Budapest, Hungary, 1999), updated now to Memory of Professor Gyula Strommer. Our intention is to illustrate interactions of Algebra, Analysis and Geometry via algorithmic and computational methods in a classical field of Geometry and of Mathematics, in general.

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