Necessary and sufficient conditions for inclusion relations for absolute summability

2003 ◽  
Vol 113 (3) ◽  
pp. 243-250
Author(s):  
B. E. Rhoades ◽  
Ekrem Savaş
Keyword(s):  
Sufficient Conditions ◽  
Absolute Summability ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Necessary And Sufficient

scholarly journals Generalized hypergeometric distribution and its applications on univalent functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rajavadivelu Themangani ◽  
Saurabh Porwal ◽  
Nanjundan Magesh
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Hypergeometric Distribution ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Necessary And Sufficient

AbstractThe purpose of the present paper is to introduce a generalized hypergeometric distribution and obtain some necessary and sufficient conditions for generalized hypergeometric distribution series belonging to certain classes of univalent functions associated with the conic domains. We also investigate some inclusion relations. Finally, we discuss an integral operator related to this series.

Absolute Summability Factors in a Sequence

1984 ◽  
Vol 27 (1) ◽  
pp. 16-30
Author(s):  
S. Baron
Keyword(s):  
Sufficient Conditions ◽  
Absolute Summability ◽  
Necessary And Sufficient Conditions ◽  
Summability Factors ◽  
Absolute Summability Factors ◽  
Necessary And Sufficient ◽  
Cesàro Method

AbstractLet α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method CαAnother theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and B=(bnk) satisfying , where (ξnk) = (ank)-1.

Generalized Markov Projections and Matrix Summability

1979 ◽  
Vol 22 (3) ◽  
pp. 311-316 ◽  
Author(s):  
Robert E. Atalla
Keyword(s):  
Sufficient Conditions ◽  
Markov Operator ◽  
Necessary And Sufficient Conditions ◽  
Averaging Operators ◽  
Matrix Summability ◽  
Markov Operators ◽  
Main Application ◽  
Summability Methods ◽  
Inclusion Relations ◽  
Necessary And Sufficient

In [A1] is defined a class of Markov operators on C(X) (X compact T2), called Generalized Averaging Operators (g.a.o.) which yield an easy solution to the following problem: given a fixed Markov operator T, find necessary and sufficient conditions on any other Markov operator R for the relation ker T ⊂ker R to hold. The main application of this is to inclusion relations between matrix summability methods.

scholarly journals Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

2019 ◽  
Vol 7 (1) ◽  
pp. 246-256 ◽  
Author(s):  
C. Marijuán ◽  
M. Pisonero ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inverse Eigenvalue Problem ◽  
Real Matrix ◽  
Real Numbers ◽  
The Real ◽  
Inclusion Relations ◽  
Inverse Eigenvalue ◽  
Necessary And Sufficient

Abstract The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in [11] a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in [11].

scholarly journals Subclass of analytic functions associated with Pascal distribution series

2021 ◽  
Vol 13(62) (2) ◽  
pp. 521-528
Author(s):  
B. A. Frasin ◽  
G. Murugusundaramoorthy ◽  
S. Yalcin
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Pascal Distribution ◽  
Necessary And Sufficient

In this paper, we find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes Wδ(α, γ, β) of analytic functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

scholarly journals On certain subclasses of analytic functions associated with Poisson distribution series

2019 ◽  
Vol 11 (1) ◽  
pp. 78-86 ◽  
Author(s):  
B. A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

Abstract In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series $\mathcal{K}\left( {{\rm{m, z}}} \right) = {\rm{z + }}\sum\limits_{{\rm{n}} = 2}^\infty {{{{{\rm{m}}^{{\rm{n}} - 1}}} \over {\left( {n - 1} \right)!}}{{\rm{e}}^{ - {\rm{m}}}}{{\rm{z}}^{\rm{n}}}} $ to be in the subclasses 𝒮(k, λ) and 𝒞(k, λ) of analytic functions with negative coefficients. Further, we obtain necessary and sufficient conditions for the integral operator ${\rm{\mathcal{G}}}\left( {{\rm{m}},{\rm{z}}} \right) = \int_0^{\rm{z}} {{{{\rm{\mathcal{F}}}\left( {{\rm{m}},{\rm{t}}} \right)} \over {\rm{t}}}} {\rm{dt}}$ to be in the above classes.

Inclusion relations for Riesz typical means

1972 ◽  
Vol 72 (3) ◽  
pp. 417-423 ◽  
Author(s):  
A. Jakimovski ◽  
J. Tzimbalario
Keyword(s):  
Sufficient Conditions ◽  
Summability Method ◽  
Necessary And Sufficient Conditions ◽  
Schauder Basis ◽  
Inclusion Relations ◽  
Necessary And Sufficient

AbstractNecessary and sufficient conditions for sequence-to-sequence or sequence-to-function summability method to include (R, λ, α), when 1 < α ≤ 2, are given. Also, for suitably restricted sequences λ, necessary and sufficient conditions for a series-to-sequence or series-to-function summability method to include (R, λ, α) for 1 < α ≤ 2 are given. These results are obtained by showing that a certain sequence {δj} (j ≥ 0) is a Schauder-basis in Rλα(N) for each α, 1 < α ≤ 2.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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