]>
2023
16
1
ISSN 2008-1898
77
Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings
Two inertial CQ-algorithms for generalized split inverse problem of infinite family of demimetric mappings
en
en
In this paper, two new inertial CQ-algorithms with strong convergence results are constructed to approximate the solution of the generalized split common fixed point problem: given as a task of finding a point that belongs to the intersection of an infinite family of fixed point sets of demimetric mappings such that its image under an infinite number of linear transformations belongs to the intersection of another infinite family of fixed point sets of demimetric mappings in the image space. The algorithms are established based on the CQ-projection method with inertial effect and step-size selection technique so that the implementation of the proposed algorithms does not need any prior information about the operator norms. The proposed methods improve, complement, and generalize many of the important results in the literature.
1
17
C.
Suanoom
Program of Mathematics, Science and Applied Science center, Faculty of Science and Technology
Kamphaeng Phet Rajabhat
Thailand
cholatis.suanoom@gmail.com
S. E.
Yimer
Department of Mathematics, College of Computational and Natural Science
Debre Berhan University
Ethiopia
seifuendris@gmail.com
A. G.
Gebrie
Department of Mathematics, College of Computational and Natural Science
Debre Berhan University
Ethiopia
antgetm@gmail.com
Split common fixed-point problem
\(\kappa\)-demimetric mapping
inertial term
CQ-algorithm
Hilbert space
strong convergence
Article.1.pdf
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[1]
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A. G. Gebrie, Weak and strong convergence adaptive algorithms for generalized split common fixed point problems, Optimization, 71 (2022), 3711-3736
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Z. He, The split equilibrium problem and its convergence algorithms, J. Inequal. Appl., 2012 (2012), 1-15
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L.-J. Qin, G. Wang, Multiple-set split feasibility problems for a finite family of demicontractive mappings in Hilbert spaces, Math. Inequal. Appl., 16 (2013), 1151-1157
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W. Takahashi, The split common fixed point problem and the shrinking projection method in Banach spaces, J. Convex Anal., 24 (2017), 1015-1028
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]
On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter
On Gould-Hopper based fully degenerate Type2 poly-Bernoulli polynomials with a \(q\)-parameter
en
en
In this paper, the Gould-Hopper based fully degenerate type2 poly-Stirling
polynomials of the first kind with a \(q\) parameter are considered and some
of their diverse identities and properties are investigated. Then, the
Gould-Hopper based fully degenerate type2 poly-Bernoulli polynomials with a
\(q\) parameter are introduced and some of their properties are analyzed and
derived. Furthermore, several formulas and relations covering implicit
summation formulas, recurrence relations and symmetric property are attained.
18
29
E.
Negiz
Department of Mathematics, Faculty of Arts and Science
University of Gaziantep
Turkiye
ecemnegiz@gmail.com
M.
Acikgoz
Department of Mathematics, Faculty of Arts and Science
University of Gaziantep
Turkiye
acikgoz@gantep.edu.tr
U.
Duran
Department of Basic Sciences of Engineering, Faculty of Engineering and Natural Sciences
Iskenderun Technical University
Turkiye
mtdrnugur@gmail.com
Gould-Hopper polynomials
Bernoulli polynomials
poly-Bernoulli polynomials
degenerate Bernoulli function
Stirling numbers of the first kind
Article.2.pdf
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A. Bayad, Y. Hamahata, Polylogarithms and poly-Bernoulli polynomials, Kyushu J. Math., 65 (2011), 15-24
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M. Cenkci, T. Komatsu, Poly-Bernoulli numbers and polynomials with a q parameter, J. Number Theory, 152 (2015), 38-54
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Some discrete d-orthogonal polynomial sets, Y. B. Cheikh, A. Zaghouani, J. Comput. Appl. Math., 156 (2003), 253-263
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U. Duran, M. Acikgoz, Generalized Gould-Hopper based fully degenerate central Bell polynomials, Turkish J. Anal. Number Theory, 7 (2019), 124-134
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U. Duran, M. Acikgoz, S. Araci, Hermite based poly-Bernoulli polynomials with a q-parameter, Adv. Stud. Contemp. Math., 28 (2018), 285-296
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U. Duran, P. N. Sadjang, On Gould-Hopper-based fully degenerate poly-Bernoulli polynomials with a q-parameter, Mathematics, 7 (2019), 1-14
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W. A. Khan, A note on degenerate Hermite poly-Bernoulli numbers and polynomials, J. Class. Anal., 8 (2016), 65-76
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W. A. Khan, N. U. Khan, S. Zia, A note on Hermite poly-Bernoulli numbers and polynomials of the second kind, Turkish J. Anal. Number Theory, 3 (2015), 120-125
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T. Kim, D. S. Kim, H. Y. Kim, L.-C. Jang, Degenerate Poly-Bernoulli numbers and polynomials, Informatica, 31 (2020), 2-8
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D. S. Kim, T. K. Kim, T. Mansour, J.-J. Seo, Fully degenerate poly-Bernoulli polynomials with a q parameter, Filomat, 30 (2016), 1029-1035
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T. Kim, D. S. Kim, J.-J. Seo, Fully degenerate poly-Bernoulli numbers and polynomials, Open Math., 14 (2016), 545-556
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M. A. O¨ zarslan, Hermite-based unified Apostol-Bernoulli, Euler and Genocchi polynomials, Adv. Differ. Equ., 2013 (2013), 1-13
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M. A. Pathan, W. A. Khan, Some implicit summation formulas and symmetric identities for the generalized Hermite- Bernoulli polynomials, Mediterr. J. Math., 12 (2015), 679-695
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]
Applications of statistical Riemann and Lebesgue integrability of sequence of functions
Applications of statistical Riemann and Lebesgue integrability of sequence of functions
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en
In the present work, we propose to investigate statistical Riemann integrability, statistical Riemann summability, statistical Lebesgue integrability and statistical Lebesgue summability by means of deferred Nörlund and deferred Riesz mean. We discuss some fundamental theorems connecting these concepts with examples. As an application to our newly formed sequences, we introduce Korovkin-type approximation theorems with relevant example for positive linear operators by using Meyer-König and Zeller operators to exhibit the effectiveness of our findings.
30
40
K.
Raj
School of Mathematics
Shri Mata Vaishno Devi University
India
kuldipraj68@gmail.com
S.
Sharma
School of Mathematics
Shri Mata Vaishno Devi University
India
sonalisharma8082@gmail.com
Statistical convergence
Riemann integral
Lebesgue integral
deferred Riesz
deferred Nörlund mean
Korovkin-type approximation theorem
Article.3.pdf
[
[1]
A. Altın, O. Do˘gru, F. Tas¸delen, The generalization of Meyer-K¨onig and Zeller operators by generating functions, J. Math. Anal. Appl., 312 (2005), 181-194
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K. Demirci, F. Dirik, S. Yıldız, Deferred N¨orlund statistical relative uniform convergence and Korovkin-type approximation theorem, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 70 (2021), 279-289
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S. A. Mohiuddine, B. A. S. Alamri, Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 1955-1973
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S. A. Mohiuddine, A. Asiri, B. Hazarika, Weighted statistical convergence through difference operator of sequences of fuzzy numbers with application to fuzzy approximation theorems, Int. J. Gen. Syst., 48 (2019), 492-506
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P. K. Nath, B. C. Tripathy, Statistical convergence of complex uncertain sequences defined by Orlicz function, Proyecciones, 39 (2020), 301-315
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K. Raj, A. Choudhary, Relative modular uniform approximation by means of the power series method with applications, Rev. Un. Mat. Argentina, 60 (2019), 187-208
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K. Saini, K. Raj, Application of statistical convergence in complex uncertain sequence via deferred Reisz mean, Int. J. Uncertain. Fuzziness Knowlege-Based Syst., 29 (2021), 337-351
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K. Saini, K. Raj, M. Mursaleen, Deferred Ces`aro and deferred Euler equi-statistical convergence and its applications to Korovkin-type approximation theorem, Int. J. Gen. Syst., 50 (2021), 567-579
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H. M. Srivastava, M. Et, Lacunary statistical convergence and strongly lacunary summable functions of order , Filomat, 31 (2017), 1573-1582
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H. M. Srivastava, B. B. Jena, S. K. Paikray, U. K. Misra, Generalized equi-statistical convergence of the deferred N¨orlund summability and its applications to associated approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 112 (2018), 1487-1501
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]
Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables
Deferred Nörlund statistical convergence in probability, mean and distribution for sequences of random variables
en
en
We introduce and study deferred Nörlund statistical convergence in probability, mean of order \(r\), distribution and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin-type theorems for the sequence of random variables via deferred Nörlund statistically convergence and present compelling examples to demonstrate the effectiveness of the results.
41
50
K.
Raj
School of Mathematics
Shri Mata Vaishno Devi University
India
kuldipraj68@gmail.com
S.
Jasrotia
School of Mathematics
Shri Mata Vaishno Devi University
India
swatijasrotia12@gmail.com
Probability convergence
Deferred Nörlund
Mean convergence
Distribution convergence
Statistical convergence
Article.4.pdf
[
[1]
A. Altin, O. Doˇgru and F. Tas¸delen, The generalization of Meyer-K¨onig and Zeller operators by generating functions, J. Math. Anal. Appl., 312 (2005), 181-194
##[2]
H. Dutta, S. K. Paikray and B. B. Jena, On statistical deferred Ces`aro summability, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications. Birkh¨auser, Cham, 487 (2019), 885-909
##[3]
A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9 (2015), 2529-2534
##[4]
M. Et, P. Baliarsingh and H. Sengul, Deferred statistical convergence and strongly deferred summable functions, AIP Conf. Proc., 2183 (2019), -
##[5]
D. Eunice Jemima, V. Srinivasan, Norlund statistical convergence and Tauberian conditions for statistical convergence from statistical summability using Norlund means in non-Archimedean fields, Journal of Mathematics and Computer Science, 24 (2022), 299-307
##[6]
H. Fast, Sur la convergence statistique, Colloquium Mathematicae, 2 (1951), 241-244
##[7]
J. A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313
##[8]
A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain Journal of Mathematics, 32 (2002), 129-138
##[9]
S. Ghosal, Statistical convergence for a sequence of random variables and limit theorems, Appl. Math. (Prague), 58 (2013), 423-437
##[10]
B. Hazarika, N. Subramanian, and M. Mursaleen, Korovkin-type approximation theorem for Bernstein operator of rough statistical convergence of triple sequences, Adv. Oper. Theory, 5 (2020), 324-335
##[11]
S. Jasrotia, U. P. Singh and K. Raj, Applications of Statistical Convergence of order ( , + ) in difference sequence spaces of fuzzy numbers, J. Intell. Fuzzy Systems, 40 (2021), 4695-4703
##[12]
B. B. Jena, S. K. Paikray and H. Dutta, On Various New Concepts of Statistical Convergence for Sequences of Random Variables via Deferred Ces`aro Mean, J. Math. Anal. Appl., 487 (2020), -
##[13]
V. A. Khan, H. Fatima, M. D. Khan, A. Ahamd, Spaces of neutrosophic -statistical convergence sequences and their properties, Journal of Mathematics and Computer Science, 23 (2021), 1-9
##[14]
S. A. Mohiuddine and B. A. S. Alamri, Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 113 (2019), 1955-1973
##[15]
S. A. Mohiuddine, A. Alotaibi and M. Mursaleen, Statistical convergence of double sequences in locally solid Riesz spaces, Abstr. Appl. Anal., 2012 (2012), -
##[16]
S. A. Mohiuddine, A. Alotaibi, and M. Mursaleen, Statistical summability (C, 1) and a Korovkin type approximation theorem, J. Inequal. Appl., 2012 (2012), 1-8
##[17]
M. Mursaleen, V. Karakaya, M. Ert ¨ urk and F G¨ ursoy, Weighted statistical convergence and its application to Korovkin type approximation theorem, Adv. Oper. Theory, 218 (2012), 9132-9137
##[18]
M. Mursaleen, Applied Summability Methods, Springer Briefs. Springer, New York (2014)
##[19]
K. Raj and A. Choudhary, Relative modular uniform approximation by means of the power series method with applications, Rev. Un. Mat. Argentina, 60 (2019), 187-208
##[20]
K. Raj and S. Pandoh, Some vector-valued statistical convergent sequence spaces, Malaya J. Mat., 3 (2015), 161-167
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D. Rath and B. C. Tripathy, Matrix maps on sequence spaces associated with sets of integers, Indian J. Pure Appl. Math., 27 (1996), 197-206
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I. J. Schoenberg, The integrability of certain functions and related summability methods, The American Mathematical Monthly, 66 (1959), 361-775
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H. M. Srivastava, B. B. Jena, S. K. Paikray and U. K. Misra, Generalized equi-statistical convergence of the deferred N¨orlund summability and its applications to associated approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 112 (2018), 1487-1501
##[24]
H. M. Srivastava, B. B. Jena, S. K. Paikray, Statistical probability convergence via the deferred N¨orlund mean and its applications to approximation theorems, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM, 114 (2020), 1-14
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H. M. Srivastava, B. B. Jena, S. K. Paikray, Deferred Ces`aro statistical probability convergence and its applications to approximation theorems, J. Nonlinear Convex Anal., 20 (2019), 1777-1792
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H. M. Srivastava, B. B. Jena and S. K. Paikray, A certain class of statistical probability convergence and its applications to approximation theorems, Appl. Anal. Discrete Math., 14 (2020), 579-598
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B.C. Tripathy, A. Esi and T. Balakrushna, On a new type of generalized difference Ces`aro sequence spaces, Soochow J. Math., 31 (2005), 333-340
]
On the analytic and approximate solutions for the fractional nonlinear Schrödinger equations
On the analytic and approximate solutions for the fractional nonlinear Schrödinger equations
en
en
In this work, we are devoted to the following fractional nonlinear Schrödinger equation with the initial conditions in the Caputo sense for \(1 < \alpha \leq 2\):
\begin{equation}\label{J1}
\begin{cases}
\displaystyle i \frac{ _c \partial^{\alpha}}{\partial \theta^{\alpha}} W(\theta, \sigma) + \beta_1 \frac{ \partial^{2}}{\partial \sigma^{2}} W(\theta, \sigma) \\
\hspace{0.5in} + \gamma (\theta, \sigma) W(\theta, \sigma) + \beta_2 |W(\theta, \sigma)|^2 W (\theta, \sigma) + \beta_3 W^2 (\theta, \sigma) = 0,\\
W(0, \sigma) = \phi_1(\sigma), \quad W_\theta'(0, \sigma) = \phi_2(\sigma),
\end{cases}
\end{equation}
where \(\theta > 0, \sigma \in \mathbb{R}\), \(\gamma(\theta, \sigma)\) is a continuous function and \(\beta_1, \beta_2, \beta_3\) are constants. Our analysis for deriving analytic and approximate solutions to the Schrödinger equation relies on the Adomian decomposition method and fractional calculus. Several illustrative examples are presented to demonstrate the solution constructions. Finally, the variant and symmetric system of the fractional nonlinear Schrödinger equations are studied.
51
59
C.
Li
Department of Mathematics and Computer Science
Brandon University
Canada
lic@brandonu.ca
K.
Nonlaopon
Department of Mathematics, Faculty of Science
Khon Kaen University
Thailand
nkamsi@kku.ac.th
A.
Hrytsenko
Department of Mathematics and Computer Science
Brandon University
Canada
hrytsea32@gmail.com
J.
Beaudin
Department of Mathematics and Computer Science
Brandon University
Canada
beaudinj@brandonu.ca
Adomian's decomposition method
Fractional nonlinear Schrödinger equation
Fractional calculus
Approximate solution
Article.5.pdf
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[1]
A. Atangana, Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system, Chaos Solitons Fractals, 102 (2017), 396-406
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A. R. Seadawy, D. Lu, C. Yue, Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability, J. Taibah Univ. Sci., 11 (2017), 623-633
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M. A. Helal, A. R. Seadawy, M. H. Zekry, Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation, Appl. Math. Comput., 232 (2014), 1-1094
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S. Vlase, M. Marin, A. Ochsner, Scutaru ML., Motion equation for a flexible onedimensional element used in the dynamical analysis of a multibody system, Contin. Mech. Thermodyn., 31 (2019), 715-724
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B. Malomed, Nonlinear Schr¨odinger equations. In Scott, Alwyn (ed.), Encyclopedia of Nonlinear Science, , New York: Routledge (2005)
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S. Z. Rida, H. M. El-Sherbinyb, A. A. M. Arafa, On the solution of the fractional nonlinear Schr¨odinger equation, Phys. lett. A, 372 (2008), 553-558
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A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam (2006)
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C. Li, R. Saadati, R. Srivastava, J. Beaudin, On the boundary value problem of nonlinear fractional integro-differential equations, Mathematics, 10 (2020), 1-14
]
Auto-oscillation of a generalized Gause type model with a convex contraint
Auto-oscillation of a generalized Gause type model with a convex contraint
en
en
In this paper, we study the generalized Gause model in which the functional and numerical responses of the predators need not be monotonic functions and the intrinsic mortality rate of the predators is a variable function. As a result, we have established sufficient conditions for the existence, uniqueness and global stability of limit cycles confined in a closed convex nonempty set, by relying on a recent Lobanova and Sadovskii theorem. Moreover, we prove sufficient conditions for the existence of Hopf bifurcation. Eventually using scilab, we illustrate the validity of the results with numerical simulations.
60
78
G. A.
Degla
Institut of Mathematics and Physical Sciences (IMSP)
University of Abomey Calavi
Benin Republic
gdegla@imsp-uac.org
S. J.
Degbo
Institut of Mathematics and Physical Sciences (IMSP)
University of Abomey Calavi
Benin Republic
jean-marie.degbo@imsp-uac.org
M.
Dossou-Yovo
Institut of Mathematics and Physical Sciences (IMSP)
University of Abomey Calavi
Benin Republic
Generalized Gause model
nonmonotonic numerical responses
nonconstant death rate
convex constraint
global stability
limit cycle
Hopf bifurcation
first Lyapunov number
Article.6.pdf
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