scholarly journals A study of Hilfer-Katugampola type pantograph equations with complex order

2022 ◽  
Vol 2 ◽  
pp. 100045
Author(s):  
S. Harikrishnan ◽  
E.M. Elsayed ◽  
K. Kanagarajan ◽  
D. Vivek
Keyword(s):  
Complex Order

scholarly journals Eisenstein series and an asymptotic for the K-Bessel function

2021 ◽  
Author(s):  
Jimmy Tseng
Keyword(s):  
Asymptotic Expansion ◽  
Bessel Function ◽  
Eisenstein Series ◽  
Uniform Estimate ◽  
Positive Real ◽  
Dominant Term ◽  
Complex Order ◽  
Fixed Parameter ◽  
Real Argument ◽  
Real Analytic

AbstractWe produce an estimate for the K-Bessel function $$K_{r + i t}(y)$$ K r + i t ( y ) with positive, real argument y and of large complex order $$r+it$$ r + i t where r is bounded and $$t = y \sin \theta $$ t = y sin θ for a fixed parameter $$0\le \theta \le \pi /2$$ 0 ≤ θ ≤ π / 2 or $$t= y \cosh \mu $$ t = y cosh μ for a fixed parameter $$\mu >0$$ μ > 0 . In particular, we compute the dominant term of the asymptotic expansion of $$K_{r + i t}(y)$$ K r + i t ( y ) as $$y \rightarrow \infty $$ y → ∞ . When t and y are close (or equal), we also give a uniform estimate. As an application of these estimates, we give bounds on the weight-zero (real-analytic) Eisenstein series $$E_0^{(j)}(z, r+it)$$ E 0 ( j ) ( z , r + i t ) for each inequivalent cusp $$\kappa _j$$ κ j when $$1/2 \le r \le 3/2$$ 1 / 2 ≤ r ≤ 3 / 2 .

scholarly journals Coefficient bounds for some families of starlike and convex functions of complex order

2007 ◽  
Vol 20 (12) ◽  
pp. 1218-1222 ◽  
Author(s):  
Osman Altıntaş ◽  
Hüseyin Irmak ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Convex Functions ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions ◽  
Complex Order

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 675 ◽  
Author(s):  
Serkan Araci ◽  
Waseem Khan ◽  
Kottakkaran Nisar
Keyword(s):  
Bernoulli Polynomials ◽  
Dirichlet Character ◽  
Bernoulli Numbers ◽  
Complex Order ◽  
Arbitrary Complex ◽  
Symmetric Identities

We aim to introduce arbitrary complex order Hermite-Bernoulli polynomials and Hermite-Bernoulli numbers attached to a Dirichlet character χ and investigate certain symmetric identities involving the polynomials, by mainly using the theory of p-adic integral on Z p . The results presented here, being very general, are shown to reduce to yield symmetric identities for many relatively simple polynomials and numbers and some corresponding known symmetric identities.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

LANGUAGES WITH A FINITE ANTIDICTIONARY: SOME GROWTH QUESTIONS

2014 ◽  
Vol 25 (08) ◽  
pp. 937-953
Author(s):  
ARSENY M. SHUR
Keyword(s):  
Growth Rate ◽  
Structural Properties ◽  
Exponential Growth ◽  
Regular Languages ◽  
The Other ◽  
Exponential Growth Rate ◽  
Strong Component ◽  
Order Of Growth ◽  
Finite Sets ◽  
Complex Order

We study FAD-languages, which are regular languages defined by finite sets of forbidden factors, together with their “canonical” recognizing automata. We are mainly interested in the possible asymptotic orders of growth for such languages. We analyze certain simplifications of sets of forbidden factors and show that they “almost” preserve the canonical automata. Using this result and structural properties of canonical automata, we describe an algorithm that effectively lists all canonical automata having a sink strong component isomorphic to a given digraph, or reports that no such automata exist. This algorithm can be used, in particular, to prove the existence of a FAD-language over a given alphabet with a given exponential growth rate. On the other hand, we give an example showing that the algorithm cannot prove non-existence of a FAD-language having a given growth rate. Finally, we provide some examples of canonical automata with a nontrivial condensation graph and of FAD-languages with a “complex” order of growth.

scholarly journals Hankel determinant for a class of analytic functions of complex order defined by convolution

2015 ◽  
Vol 69 (2) ◽  
pp. 47
Author(s):  
S. M. El-Deeb ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Upper Bounds ◽  
Hankel Determinant ◽  
Complex Order ◽  
Second Hankel Determinant

In this paper, we obtain the Fekete-Szego inequalities for the functions of complex order defined by convolution. Also, we find upper bounds for the second Hankel determinant \(|a_2a_4-a_3^2|\) for functions belonging to the class \(S_{\gamma}^b(g(z);A,B)\).

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