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The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

ARAL, Ali/0000-0002-2024-8607; Gupta, Vijay/0000-0002-5768-5763 WOS:000565809500015 In the present paper we establish a general form of Voronovskaja's theorem for functions defined on an unbounded interval and having exponential growth. The case of approximation by linear combinations is also considered. Applications are given for some Szasz-Mirakyan and Baskakov-type operators.

EgeUn###, For a locally integrable function f on [ 0, ?), we define F(t) = ? t 0 f(u)du and ? ? (t) = ? t 0 (1 - u t) ? (u)du for t > 0. The improper integral ? ? 0 f(u)du is said to be (C, ?) integrable to L for some ? > - 1 if the limit lim x › ? ? ?(t) = L exists. It is known that lim t › ? F(t) = l implies lim t › ? ? ?(t) = l for ? > - 1, but the converse of this implication is not true in general. In this paper, we introduce the concept of the general control modulo of non-integer order for functions and obtain some Tauberian conditions in terms of this concept for the (C, ?) integrability method in order that the converse implication hold true. Our results extend the main theorems in [Ü. Totur and I. Çanak, Tauberian conditions for the (C, ?) integrability of functions, Positivity 21 2017, 1, 73-83]. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019.

Made available in DSpace on 2020-12-10T16:57:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-10-01 In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice. (C) 2019 Mathematical Institute Slovak Academy of Sciences Tanta Univ, Fac Sci, Dept Math, Tanta, Egypt State Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil Kohat Univ Sci & Technol, Dept Math, Kohat 26000, Pakistan State Univ Sao Paulo, Dept Stat, Sao Paulo, Brazil

Gogatishvili, Amiran/0000-0003-3459-0355; Yildiz, Tugce Unver/0000-0003-0414-8400; Gogatishvili, Amiran/0000-0003-3459-0355 WOS: 000503861600008 In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Cop(p1), (q1) ((u1,) (v1)) and weighted Cesaro function spaces Ces(p2, q2) (u(2), v(2)) is presented, where p(1), p(2), q(1), q(2) is an element of (0,infinity), p(2)

Kunt, Mehmet/0000-0002-8730-5370; iscan, imdat/0000-0001-6749-0591 WOS: 000476630200006 In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.

In this paper, we study the Riesz potential (G-Riesz potential) generated by the Gegenbauer differential operator G λ = ( x 2 - 1 ) 1 2 - λ ⁢ d d ⁢ x ⁢ ( x 2 - 1 ) λ + 1 2 ⁢ d d ⁢ x , x ∈ ( 1 , ∞ ) , λ ∈ ( 0 , 1 2 ) . G_{\lambda}=(x^{2}-1)^{\frac{1}{2}-\lambda}\frac{d}{dx}(x^{2}-1)^{\lambda+% \frac{1}{2}}\frac{d}{dx},\quad x\in(1,\infty),\,\lambda\in\Bigl{(}0,\frac{1}{2% }\Bigr{)}. We prove that the G-Riesz potential I G α {I_{G}^{\alpha}} , 0 < α < 2 ⁢ λ + 1 {0 , is bounded from the G-Morrey space L p , λ , γ {L_{p,\lambda,\gamma}} to L q , λ , γ {L_{q,\lambda,\gamma}} if and only if 1 p - 1 q = α 2 ⁢ λ + 1 - γ , 1 < p < 2 ⁢ λ + 1 - γ α . \frac{1}{p}-\frac{1}{q}=\frac{\alpha}{2\lambda+1-\gamma},\quad 1 Also, we prove that the G-Riesz potential I G α {I_{G}^{\alpha}} is bounded from the G-Morrey space L 1 , λ , γ {L_{1,\lambda,\gamma}} to the weak G-Morrey space W ⁢ L q , λ , γ {WL_{q,\lambda,\gamma}} if and only if 1 - 1 q = α 2 ⁢ λ + 1 - γ . 1-\frac{1}{q}=\frac{\alpha}{2\lambda+1-\gamma}.

In this paper, using the concept of ideal convergence, which extends the idea of ordinary convergence and statistical convergence, we are concerned with the I-uniform convergence and the I-pointwise convergence of sequences of functions defined on a set of real numbers D. We present the Arzelà–Ascoli theorem by means of ideal convergence and also the relationship between I-equicontinuity and I-continuity for a family of functions.

In this paper, we study the boundedness of the Hardy operators on Musielak–Orlicz spaces.

SET, ERHAN/0000-0003-1364-5396; Akdemir, Ahmet Ocak/0000-0003-2466-0508 WOS: 000426436000011 In this paper, we establish Ostrowski-type inequalities for strongly convex functions, by using some classical inequalities and elementary analysis. We also give some results for the product of two strongly convex functions.

This paper deals with the asymptotic behavior of the sequence of codimensions c n ⁢ ( A ) ${c_{n}(A)}$ , n = 1 , 2 , … , ${n=1,2,\ldots,}$ of an algebra A over a field of characteristic zero. It is shown that when such sequence is polynomially bounded, then lim sup n → ∞ ⁡ log n ⁡ c n ⁢ ( A ) ${\limsup_{n\to\infty}\log_{n}c_{n}(A)}$ and lim inf n → ∞ ⁡ log n ⁡ c n ⁢ ( A ) ${\liminf_{n\to\infty}\log_{n}c_{n}(A)}$ can be arbitrarily distant. Also, in case the codimensions are exponentially bounded, we can construct an algebra A such that exp ⁡ ( A ) = 2 ${\exp(A)=2}$ and, for any q ≥ 1 ${q\geq 1}$ , there are infinitely many integers n such that c n ⁢ ( A ) > n q ⁢ 2 n ${c_{n}(A)>n^{q}2^{n}}$ . This gives counterexamples to a conjecture of Regev for both cases of polynomial and exponential codimension growth.

In [Acta Math. Hungar. 66 (1995), 337–343], Bell and Daif proved that if R is a prime ring admitting a nonzero derivation such that d ( x y ) = d ( y x ) ${d(xy)=d(yx)}$ for all x , y ∈ R ${x,y\in R}$ , then R is commutative. The objective of this paper is to examine similar problems when the ring R is equipped with involution. It is shown that if a prime ring R with involution * of a characteristic different from 2 admits a nonzero derivation d such that d ( x x * ) = d ( x * x ) ${d(xx^*)=d(x^*x)}$ for all x ∈ R and S ( R ) ∩ Z ( R ) ≠ ( 0 ) ${S(R)\cap Z(R)\ne (0)}$ , then R is commutative. Moreover, some related results have also been discussed.

WOS: 000398461200003, Let R be a ring and I is a nonzero ideal of R. A mapping F : R -> R is called a multiplicative generalized derivation if there exists a mapping g : R -> R such that F(xy) = F(x)y + xg(y), for all x, y is an element of R. In the present paper, we shall prove that R contains a nonzero central ideal if any one of the following holds: i) F([x, y]) = 0, vii) F([x, y]) = +/-[F(x), y], ii) F(x circle y) = 0, viii) F(x circle y) = +/-(F(x)circle y), iii) F([x, y]) = +/-[x, y], ix) F(xy) +/- xy is an element of Z, iv) F(x circle y) =+/-(x circle y), x) F(xy)+/- yx is an element of Z, v) F([x, y]) = +/-(x circle y), xi) F(xy) +/- [x, y]is an element of Z, vi) F(x circle y) = +/-[x, y], xii) F(xy) +/- (x circle y)is an element of Z, for all x, y is an element of I. (C) 2016 Mathematical Institute Slovak Academy of Sciences

The classical Korovkin approximation theory deals with the convergence of a given sequence { L n } ${\lbrace L_{n}\rbrace }$ of positive linear operators on C[a,b]. When the sequence of positive linear operators does not converge to the identity operator it may be useful to use some summability methods. In this paper, we study some Korovkin type approximation theorems for the sequences of convolution operators via the Abel method, which is a sequence-to-function transformation. We also deal with the rate of Abel convergence.

Let T denote the interval [-?,?]. IN this paper, some theorems for approximation by trigonometric polynomials in the Orlicz space LM(T) are proved. Under certain conditions, we prove the existence of derivatives of functions belonging to the Orlicz space LM(T) and investigate the approximation properties of the derivatives of trigonometric polynomials. Note that the estimate obtained between the derivatives of functions and the derivatives of trigonometric polynomials depends on a sequence of best approximations in the Orlicz space LM(T). © 2012, by Walter de Gruyter Berlin Boston. All rights reserved.

In the present paper we propose a generalization of the Baskakov operators, based on q integers. We also estimate the rate of convergence in the weighted norm. In the last section, we study some shape preserving properties and the property of monotonicity of q-Baskakov operators.

Some modifed direct localized boundary-domain integral equations (LBDIEs) systems associated with the mixed boundary value problem (BVP) for a scalar “Laplace” PDE with variable coefficient are formulated and analyzed. The main results established in the paper are the LBDIEs equivalence to the original variable-coefficient BVPs and the invertibility of the corresponding localized boundary-domain integral operators in appropriately chosen function spaces.

In this paper, we prove a common fixed point theorem for sequences of maps under the condition of compatible mappings on complete metric space. We extend and generalize several fixed point theorems on complete metric space. © 2005 Warsaw University. All rights reserved. Gazi Üniversitesi: 05/2003-01 1991 Mathematics Subject Classification: Primary 54H25, Secondary 47H10. Key words and phrases: Fixed point, set-valued mapping, compatible mapping. This research was supported by Gazi University project no. 05/2003-01, Turkey.