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In a recent paper, Yu et al. obtained convergence and stability results of the K* iterative method for quasistrictly contractive mappings [An iteration process for a general class of contractive-like operators: Convergence, stability and polynomiography. AIMS Mathematics 2021; 6 (7): 6699-6714.]. To guarantee these convergence and stability results, the authors imposed some strong conditions on parametric control sequences which are used in the K* iterative method. The aim of the presented work is twofold: (a) to recapture the aforementioned results without any restrictions imposed on the mentioned parametric control sequences (b) to complete the work of Yu et al. by adding a result regarding the data dependency of the fixed points of quasi-strictly contractive mappings. We also furnish some illustrative examples to support our results. Our work can be considered an important refinement and complement of the work of Yu et al.

In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions

Fibonacci cubes are defined as subgraphs of hypercubes, where the vertices are those without two consecutive l's in their binary string representation. k-Fibonacci cubes are in turn special subgraphs of Fibonacci cubes obtained by eliminating certain edges. This elimination is carried out at the step analogous to where the fundamental recursion is used to construct Fibonacci cubes themselves from the two previous cubes by link edges. In this work, we calculate the vertex chromatic polynomial of k-Fibonacci cubes for k = 1,2. We also determine the domination number and the total domination number of k-Fibonacci cubes for n, k

WOS: 000488222100015 In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

WOS: 000447946800043, In this paper, matrix rings with the summand intersection property (SIP) and the absolute direct summand (ads) property (briefly, SA) are studied. A ring R has the right SIP if the intersection of two direct summands of R is also a direct summand. A right R-module M has the ads property if for every decomposition M = A circle plus B of M and every complement C of A in M, we have M = A circle plus C. It is shown that the trivial extension of R by M has the SA if and only if R has the SA, M has the ads, and (1 - e)Me = 0 for each idempotent e in R. It is also shown with an example that the SA is not a Morita invariant property., Anadolu University Scientific Research Projects Commission [1503F139], This study was supported by Anadolu University Scientific Research Projects Commission under the grant no: 1503F139.

Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper, we assume that $P$ and $Q$ are relatively prime odd positive integers and $P^{2}+4Q>0.$ We determine all indices $n$ such that $U_{n}=(P^{2}+4Q)x^{2}.$ Moreover, we determine all indices $n$ such that $(P^{2}+4Q)U_{n}=x^{2}.$ As a result, we show that the equation $V_{n}^{2}(P,1)+V_{n+1}^{2}(P,1)=x^{2}$ has solution only for $n=2,$ $P=1,$ $x=5$ and $V_{n+1}^{2}(P,-1)=V_{n}^{2}(P,-1)+x^{2}$ has no solutions. Moreover, we solve some Diophantine equations.

WOS: 000439579600021, Vectorization is a technique that replaces a set-valued optimization problem with a vector optimization problem. In this work, by using an extension of the Gerstewitz function, a vectorizing function is defined to replace a given set-valued optimization problem with respect to the set less order relation. Some properties of this function are studied. Moreover, relationships between a set-valued optimization problem and a vector optimization problem, derived via vectorization of this set-valued optimization problem, are examined. Furthermore, necessary and sufficient optimality conditions are presented without any convexity assumption.

It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal interpolation function to the graph-directed case and prove that for a finite number of data sets there exist interpolation functions each of which interpolates corresponding data set in $\mathbb{R}^2$ such that the graphs of the interpolation functions are attractors of a graph-directed iterated function system., Comment: 14 pages

Sums of products of two Gaussian q-binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.

WOS: 000406419900023, We study almost contact metric structures induced by 2-fold vector cross products on manifolds with G(2) structures. We get some results on possible classes of almost contact metric structures. Finally, we give examples., Anadolu University Scientific Research Projects Commission [1501F017], This study was supported by the Anadolu University Scientific Research Projects Commission under Grant No : 1501F017.

In this paper, by considering a Frenet curve lying on an oriented hypersurface, we extend the Darboux frame field into Euclidean 4 -space E-4. Depending on the linear independency of the curvature vector with the hypersurface's normal, we obtain two cases for this extension. For each case, we obtain some geometrical meanings of new invariants along the curve on the hypersurface. We also give the relationships between the Frenet frame curvatures and Darboux frame curvatures in E-4. Finally, we compute the expressions of the new invariants of a Frenet curve lying on an implicit hypersurface. Yıldız Teknik Üniversitesi- 2013-01-03-KAP01

In this paper, some properties of Riesz space valued measures that are defined on an algebra of sets are obtained. The question of under what conditions $oba(\mathcal{F},E)$ =$a(\mathcal{F},E)$ for a given Dedekind complete Riesz space $E$ is answered under natural conditions. The outer measure, which is generated by order bounded Riesz space valued measure, is obtained and its properties are investigated. The concept of hazy convergence that is valid for real valued signed measures is extended to Riesz space valued measures. The consequences of order convergence of $f:X\rightarrow E$, which implies hazy convergence, are given.

other A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral. A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transformation of these sequences by a summability matrix. We also present some further results via the Lebesgue integral.

WOS: 000439014600029 In this paper, we study the position vector of a spacelike rectifying slant helix with non-lightlike principal normal vector field in E1(3). First we find the general equations of the curvature and the torsion of spacelike rectifying slant helices. After that, we construct second-order linear differential equations. By their solutions, we determine families of spacelike rectifying slant helices that lie on cones. Ahi Evran UniversityAhi Evran University [PYO-EGF.4001.15.001] This research was supported by Ahi Evran University: PYO-EGF.4001.15.001.

In this paper, we will investigate and evaluate, in closed forms, three binomial sums weighted by falling and rising factorials. We first use the relationships between the rising, falling factorials and the binomial coefficients. Then we rewrite the claimed identities in terms of generalized hypergeometric functions to prove the claimed results.

A finite group F H is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that F H/[F, F] is a Frobenius group with Frobenius kernel F/[F, F]. Such subgroups and sections are abundant in any nonnilpotent finite group. We discuss several recent results about the properties of a finite group G admitting a Frobenius-like group of automorphisms F H aiming at restrictions on G in terms of CG(H) and focusing mainly on bounds for the Fitting height and related parameters. Earlier such results were obtained for Frobenius groups of automorphisms; new theorems for Frobenius-like groups are based on new representation-theoretic results. Apart from a brief survey, the paper contains the new theorem on almost nilpotency of a finite group admitting a Frobenius-like group of automorphisms with fixed-point-free almost extraspecial kernel.

The main interest of the present paper is to classify the almost cosymplectic 3-manifolds that satisfy parallel to grad lambda parallel to All = const.(not equal 0) and del xi h = 2ah phi.

In this work, we investigate the solvability of the problem partial derivative(2)w/partial derivative(phi) over bar (2) = f Re{i phi(z)w(z)} = gamma(1)(z), Rew((phi) over bar)(z) = gamma(2)(z) z is an element of partial derivative D in the unit disk of complex plane. Here f, gamma(1) and gamma(2) are given m x s-complex matrix-valued functions; f is an element of L(p)((D) over bar), gamma(1), gamma(2) is an element of C(partial derivative D) and phi is a generating solution for Q-holomorphic functions.

WOS: 000284435200014, We discuss how chaos conditions on maps carry over to their products First we give a counterexample showing that the product of two chaotic maps (in the sense of Devaney) need not be chaotic We then remark that if two maps (or even one of them) exhibit sensitive dependence on initial conditions, so does their product, likewise, if two maps possess dense periodic points, so does their product On the other side, the product of two topologically transitive maps need not be topologically transitive We then give sufficient conditions under which the product of two chaotic maps is chaotic in the sense of Devaney [6]