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238 results on '"Canak, Ibrahim"'

1. The novel Tauberian conditions associated with the $(\overline{N},p,q)$ summability of double sequences

Author

Önder, Zerrin, Savaş, Ekrem, and Çanak, İbrahim

Subjects
Mathematics - General Mathematics, 40A05, 40E05, 40G99
Abstract

In this paper, our primary objective is to provide a fresh perspective on the relationship between the $(\overline{N},p,q)$ method, which is a product of relevant one-dimensional summability methods, and $P$-convergence for double sequences. To accomplish this objective, we establish certain Tauberian conditions that control the behavior of a double sequence in terms of both $O_L$-oscillation and $O$-oscillation in certain senses, building a bridge between $(\overline{N},p,q)$ summability and $P$-convergence, while imposing certain restrictions on the weight sequences. As special circumstances of our findings, we demonstrate that Landau-type $O_L$ condition with respect to $(P_m)$ and $(Q_n),$ as well as Hardy-type $O$ condition with respect to $(P_m)$ and $(Q_n),$ serve as Tauberian conditions for $(\overline{N},p,q)$ summability under particular additional conditions. Consequently, these results encompass all classical Tauberian theorems, including conditions such as slow decrease or slow oscillation in certain senses.

Published
2023

6. Some novel approaches on the (N̅, p, q) summability of double sequences of fuzzy numbers and its applications.

Author

Onder, Zerrin, Savas, Ekrem, and Canak, Ibrahim

Subjects
FUZZY numbers, SUMMABILITY theory, POSITIVE operators, LINEAR operators
Abstract

In this paper, our aim is to make a novel interpretation of relation between (N̅,p,q) method and P-convergence for double sequences of fuzzy numbers. In accordance with this aim, we derive some Tauberian conditions, controlling O-oscillatory behavior of a double sequence of fuzzy numbers in certain senses, from (N̅,p,q) summability to P- convergence with some restrictions on the weight sequences. As special cases, we indicate that O-condition of Hardy type with respect to (Pm) and Qn are Tauberian conditions for (N̅,p,q) summability under some additional conditions. In the sequel, we prove a fuzzy Korovkin-type approximation theorem by using the (N̅,p,q) summability method for fuzzy positive linear operators. [ABSTRACT FROM AUTHOR]

Published
2023
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8. Conditions under which convergence of a sequence or its certain subsequences follows from deferred Cesàro summability

Author

Sezer, Sefa Anil, Canak, Ibrahim, and Dutta, Hemen

Subjects
deferred slow oscillation, Fourier, Tauberian conditions and theorems, Statistical Convergence, ordered linear spaces, General Mathematics, Theorems, moving averages, deferred slow decrease, Deferred Cesaro means, Sufficient Tauberian Conditions
Abstract

Let (un:n=1,2,...) be a sequence of real or complex numbers. We aim in this paper to determine necessary and/or sufficient conditions under which convergence of a sequence (un) or its certain subsequences follows from summability by deferred Ces?ro means. We also investigate the limiting behavior of deferred moving averages of (un). The conditions in our theorems are one-sided if (un) is a sequence of real numbers, and two-sided if (un) is a sequence of complex numbers. The theory developed in this paper should be useful for developing more interesting and useful results in connection with other sophisticated summability means as well as to extend to other spaces like ordered linear spaces.

Published
2022

11. On the convergence of weighted mean summable improper integrals over R->= 0

Author

Sezer, Sefa Anil and Canak, Ibrahim

Subjects
=+0%22">Improper integrals over R->= 0, Iterated weighted means, Lebesgue integral, Tauberian conditions, Tauberian-Theorems, Iterations, Weighted mean summability of integrals, Forward and backward differences
Abstract

Given a real-valued function a(x) which is locally integrable in the sense of Lebesgue Rover R->= 0, we obtain Tauberian conditions for the convergence of the integral integral(infinity)(0)a(t)dt out of the weighted mean summability. Furthermore, we discuss summability of improper integrals via iterations of weighted means and provide corresponding Tauberian theorems.

Published
2022

39. A Tauberian condition under which convergence follows from the weighted mean summability of sequences of fuzzy number

Author

Onder, Zerrin, Canak, Ibrahim, and Ege Üniversitesi

Subjects
slow decrease, Tauberian theorems, weighted mean summability method, slow decrease with respect to the ((N)over-bar,p) method, Sequences of fuzzy numbers
Abstract

Let (u(n)) be a sequence of fuzzy numbers and (p(n)) be a sequence of nonnegative numbers such that p(0 )> 0 and Pn := Sigma(n)(k=0) pk -> infinity as n -> infinity the weighted mean of (u(n)) is defined by t(n) := 1/P-n Sigma(n)(k=0) p(k )u(k) for n = 0, 1, 2, ... It is well known that convergence of (u(n)) implies that of the sequence (t(n)) of its weighted means. However, the converse of this implication is not true in general. in this paper, we investigate under which conditions convergence of (u(n)) follows from its weighted mean summability. We prove a Tauberian theorem including condition of slow decrease with respect to the weighted mean summability method for sequences of fuzzy numbers.

Published
2020

42. TAUBERIAN REMAINDER THEOREMS FOR ITERATIONS OF METHODS OF WEIGHTED MEANS

Author

Sezer, Sefa Anil, Canak, Ibrahim, and Ege Üniversitesi

Subjects
Tauberian remainder theorem, lambda-bounded sequence, weighted mean method, weighted general control modulo
Abstract

EgeUn###, In this paper we prove some Tauberian remainder theorems on lambda-bounded sequences for iterations of methods of weighted means.

Published
2019

43. Statistical extensions of Tauberian theorems for the weighted mean method of summability in two-normed spaces.

Author

Bakicierler, Hulya, Canak, Ibrahim, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
*TAUBERIAN theorems, *NORMED rings
Abstract

In this extended abstract, we first define the concept of statistical summability (N̅, p) in 2-normed spaces and then present necessary and/or sufficient Tauberian conditions for statistical summability (N̅, p) in 2-normed spaces. [ABSTRACT FROM AUTHOR]

Published
2020
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44. Hyperbolic-trigonometric tension B-spline Galerkin approach for the solution of Fisher equation.

Author

Dag, Idris, Hepson, Ozlem Ersoy, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
HYPERBOLIC differential equations, CRANK-nicolson method, FINITE element method, GALERKIN methods, EQUATIONS
Abstract

A Galerkin finite element method is constructed for computing solution of the Fisher equation. Hyperbolic-trigonometric tension (HTT) B-splines are used as weight and shape functions in the Galerkin approach. Fully discretization of the Fisher equation is fulfilled via Crank-Nicolson method in time and Galerkin method in space. Travelling wave front solution is studied to show robustness of the presented scheme on Fisher equation. The numerical results obtained with the present method are satisfactory with regard to its accuracy. [ABSTRACT FROM AUTHOR]

Published
2020
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45. Hyperbolic-trigonometric tension B-spline Galerkin approach for the solution of RLW equation.

Author

Dag, Idris, Hepson, Ozlem Ersoy, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
NONLINEAR equations, ORDINARY differential equations, GALERKIN methods, FINITE element method, EQUATIONS, SPLINE theory, TRIGONOMETRIC functions
Abstract

A numerical approach is defined to get the solution of the regularized long wave (RLW) equation. The hyperbolic- trigonometric tension (HTT) B-spline is adapted as a trial function to the Galerkin method. Space integration of the RLW equation is managed trough HTT B-spline Galerkin method over the finite elements. Resulting system of ordinary differential equations is integrated using the Crank Nicolson technique. Thus RLW equation is fully integrated into system of nonlinear algebraic equations. Solution of this system gives the approximate solution of the RLW equation over the given problem domain. [ABSTRACT FROM AUTHOR]

Published
2020
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46. Rayleigh Gamma gompertz distribution: Properties and applications.

Author

Al-Noor, Nadia Hashim, Assi, Noor Kareem, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
DISTRIBUTION (Probability theory), GAMMA distributions, CHARACTERISTIC functions, MAXIMUM likelihood statistics, WEIBULL distribution
Abstract

In this paper, Rayleigh Gamma Gompertz (RGGom), as a new compound distribution, is introduced. Various fundamental statistical properties of RGGom distribution, including explicit expressions for the non-central rth moment, characteristic function, quantile function and simulated data, Shannon and relative entropies, and reliability stress strength model, were studied and inspected. The unknown parameters of RGGom have been estimated using the estimation method of maximum likelihood. Furthermore, the RGGom distribution is applied upon a simulation study and two real-life data sets to assess its usefulness and flexibility. [ABSTRACT FROM AUTHOR]

Published
2020
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47. Maximal inequalities with exponential decay under weak dependence conditions.

Author

Boukhari, Fakhreddine, Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
MAXIMAL functions, RANDOM variables, LARGE deviations (Mathematics), LAW of large numbers, DEPENDENT variables, LOGARITHMS
Abstract

We establish large deviation inequalities with exponential decay for the maximum of partial sums of subgaussian random variables. Applying our result to acceptable sequences of bounded mean zero random variables, we strengthen a well-known inequality of Hoeffding. As a consequence we prove a bounded law of iterated logarithm for this class of random variables. The obtained method, also allows us to state a strong integrability property for weighted series of negatively dependent random variables. [ABSTRACT FROM AUTHOR]

Published
2020
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48. Marshal Olkin Marshal Olkin gompertz distribution.

Author

Al-Noor, Nadia Hashim, Khaleel, Mundher A., Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, Onvural, Oruc Raif, and Sahin, Hakan

Subjects
DISTRIBUTION (Probability theory), MAXIMUM likelihood statistics
Abstract

The aim of this paper is to propose a new flexible compound distribution named Marshal Olkin Marshal Olkin Gompertz (MOMOGo) distribution. Reliability characteristics besides several statistical properties of the proposed distribution have discussed. The maximum likelihood method, under a complete sample, is used to estimate the distribution parameters. Furthermore, two real data sets are considered to investigate the applicability of the proposed MOMOGo distribution. [ABSTRACT FROM AUTHOR]

Published
2020
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49. Modifying fractal image compression technique by hybridation of crowding genetic algorithm and scattered method.

Author

Al-Bundi, Shaimaa S., AL-Jubouri, Karrar Q., Al-Saidi, Nadia M. G., Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, and Onvural, Oruc Raif

Subjects
IMAGE compression, GENETIC algorithms, SEARCH algorithms, METAHEURISTIC algorithms
Abstract

Fractal image coding is one of the active techniques for image compression. It always motivates for designing efficient algorithms to optimize the search space and reduce computation efforts, which is the main disadvantage of this technique. Hybridizing the metaheuristic methods has a vital interest in the optimization field. In this work, an intelligent search technique based on combining of crowding genetic and scattered search methods is proposed, in which the essential steps (generating a collection of diverse trial solutions, and the combined solutions method) in scattered search replaced by the two essential steps (the recombination and the mutation) in crowding method. Satisfactory results in reducing the computation cost of the fractal image compression technique are obtained. [ABSTRACT FROM AUTHOR]

Published
2020
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50. A new design of NTRU encryption with high security and performance level.

Author

Yassein, Hassan R., Abidalzahra, Asia A., Al-Saidi, Nadia M., Cakalli, Huseyin, Kocinac, Ljubisa D. R., Ashyralyev, Allaberen, Harte, Robin, Dik, Mehmet, Canak, Ibrahim, Kandemir, Hacer Sengul, Tez, Mujgan, Gurtug, Ozay, Savas, Ekrem, Akay, Kadri Ulas, Ucgun, Filiz Cagatay, Uyaver, Sahin, Ashyralyyev, Charyyar, Sezer, Sefa Anil, Turkoglu, Arap Duran, and Onvural, Oruc Raif

Subjects
QUATERNIONS, ALGEBRA, RSA algorithm, SECURITY management
Abstract

A multi-dimensional QTRU public-key cryptosystem improves NTRU by replacing the original ring in NTRU by quaternion algebra. In this paper, we introduce QMNTR an improvement of QTRU by using a new mathematical structure of two public keys and five private keys. This modification has enhanced the public key system to be more robust and secure. [ABSTRACT FROM AUTHOR]

Published
2020
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