Volume 74 , issue 3 ( 2022 ) | back |

FIBONACCI NUMBERS WHICH ARE CONCATENATIONS OF THREE REPDIGITS | 155$-$162 |

**Abstract**

In this study, it is proved that the only Fibonacci numbers which are concatenations of three repdigits are $144$, $233$, $377$, $610$, $987$, $17711$.

**Keywords:** Fibonacci number; concatenations; repdigit; Diophantine equations; linear forms in logarithms.

**MSC:** 11B39, 11J86, 11D61

YOUNG TYPE INEQUALITIES AND REVERSES FOR MATRICES | 163$-$173 |

**Abstract**

In this paper, we give some Young type inequalities for scalars. By using these inequalities we establish corresponding Young type inequalities for matrices. In addition, we present some reverses of the Young type inequalities and give several refinements for matrices.

**Keywords:** Heinz mean inequalities; positive semidefinite matrices; Hilbert-Schmidt norm; Young inequality.

**MSC:** 26D07, 26D15, 15A18, 47A63

AN INERTIAL BREGMAN HYBRID ALGORITHM FOR APPROXIMATING SOLUTIONS OF FIXED POINT AND VARIATIONAL INEQUALITY PROBLEM IN REAL BANACH SPACES | 174$-$188 |

**Abstract**

In this work, we study an inertial extragradient-like S-iteration process for approximating a common element of the set of solutions of some variational inequality problem involving a monotone Lipschitz map and a fixed point of asymptotically nonexpansive mapping in a reflexive Banach space. The result in this paper is an extension and generalization of some recently announced results.

**Keywords:** Strong convergence; fixed point problem; variational inequality; Bregman quasi nonexpansive mappings.

**MSC:** 47H09, 47H10, 47J25

LINEAR COMBINATIONS OF UNIVALENT HARMONIC MAPPINGS WITH COMPLEX COEFFICIENTS | 189$-$196 |

**Abstract**

We study the linear combinations $f(z)= \lambda f_{1}(z)+(1-\lambda) f_{2}(z)$ of two univalent harmonic mappings $f_{1}$ and $f_{2}$ in the cases when $\lambda$ is some complex number. We determine the radius of close-to-convexity of $f$ and establish some sufficient conditions for $f$ to be locally-univalent and sense-preserving. Some known results reduce to particular cases of our general results.

**Keywords:** Univalent harmonic mappings; linear combination; convex in the horizontal direction.

**MSC:** 30C45

CLAIRAUT ANTI-INVARIANT SUBMERSIONS FROM NEARLY KÄHLER MANIFOLDS | 197$-$204 |

**Abstract**

In the present paper, we investigate geometric properties of Clairaut anti-invariant submersions whose total spaces are nearly Kähler manifolds. We obtain a condition for a Clairaut anti-invariant submersion to be a totally geodesic map and also study Clairaut anti-invariant submersions with totally umbilical fibers.

**Keywords:** Riemannian submersion; nearly Kähler manifolds; anti-invariant submersion; Clairaut submersion; totally geodesic maps.

**MSC:** 53C12, 53C15, 53C20, 53C55

SOME GENERALIZATIONS OF A THEOREM OF PAUL TURÀN CONCERNING POLYNOMIALS | 205$-$213 |

**Abstract**

Let $P(z)=\sum_{\nu=0}^n a_\nu z^\nu$ be a polynomial of degree $n$ having all its zeros in $|z|\leq k$, $ k\geq 1$. It was shown by Govil that $\underset{|z|=1}\max|P'(z)|\geq\frac{n}{1+k^n}\underset{|z|=1}\max|P(z)|$. In this paper, we shall obtain some sharp estimates by involving the coefficients which not only refine the above result but also generalise some well-known results of this type.

**Keywords:** Polynomials; inequalities in complex domain; derivative; s-fold zeros.

**MSC:** 26D10, 30C15, 41A17

COMPLEX CROFTON FORMULA | 214$-$217 |

**Abstract**

One of the initial and at the same time key formulas of integral geometry is Crofton's formula. We consider a complex version of Crofton's formula.

**Keywords:** Integral geometry; Crofton formula; complex analysis; Fubini–Study metric.

**MSC:** 53C65, 32F45

ON $\mathcal{I}$-STATISTICAL CONVERGENCE OF SEQUENCES IN GRADUAL NORMED LINEAR SPACES | 218$-$228 |

**Abstract**

In this article, we introduce the notion of $\mathcal{I}$-statistical convergence of sequences as one of the extensions of $\mathcal{I}$-convergence in the gradual normed linear spaces. We investigate some fundamental properties of the newly introduced notion and its relation with some other methods of convergence. Also we introduce and investigate the concept of $\mathcal{I}$-statistical limit points, cluster points and establish some implication relations.

**Keywords:** Gradual number; gradual normed linear spaces; statistical convergence; $\mathcal{I}$-convergence; $\mathcal{I}$-statistical convergence.

**MSC:** 03E72, 40A35, 40A05