Muhammet KAMALİ

Article | 2020 | Turkish Journal of Mathematics44 ( 3 )

In this paper, the authors investigate the initial coefficient bounds for a new generalized subclass of analytic functions related to Sigmoid functions. Also, the relevant connections with the famous classical Fekete?Szegö inequality for these classes are discussed.

Olgun DURMAZ

Article | 2023 | Turkish Journal of Mathematics47 ( 5 )

Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings. Keywords: dual numbers; dual absolute value; dual inequalities; dual norm

Fahreddin ABDULLAYEV | Meerim İmaş Kızı

Article | 2020 | Turkish Journal of Mathematics44 ( 1 )

In weighted Orlicz-type spaces S-p,S- (mu) with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is the best in a certain sense. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the spaces S-p,S- (mu).

İsmet ALTINTAŞ

Article | 2020 | Turkish Journal of Mathematics44 ( 6 )

In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additi . . .onally, we prove some fixed point theorems related to diametrically contractive mapping in a complete soft cone metric space More less

Fahreddin ABDULLAYEV

Article | 2022 | Turkish Journal of Mathematics46 ( 7 )

In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.

Muhammet KAMALİ

Article | 2021 | Turkish Journal of Mathematics45 ( 3 )

In this paper,we define a class of analytic functions F-(beta,lambda()) (H, alpha, delta, mu), satisfying the following subordinate condition associated with Chebyshev polynomials {alpha[zG' (z)/G (z)](delta) + (1 - alpha) [zG' (z)/G (z)](mu) [1 + zG '' (z)/G' (z)](1-mu)} < H (z, t), where G(z) = lambda beta z(2)f '' (z) + (lambda - beta) zf' (z) + (1 - lambda + beta) f (z) , 0

İsmet ALTINTAŞ

Article | 2023 | Turkish Journal of Mathematics47 ( 1 )

In this paper, we define a two-variable polynomial invariant of regular isotopy, M_K for a disoriented link diagram K. By normalizing the polynomial M_K using complete writhe, we obtain a polynomial invariant of ambient isotopy, N_K, for a disoriented link diagram K. The polynomial N_K is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial F to the disoriented links. Moreover, the polynomial M_K is an expansion of the Kauffman polynomial L to the disoriented links.