Serdica Mathematical Journal

Volume 47, Number 1, 2021

C O N T E N T S

A B S T R A C T S

MULTI-STEP HIGH CONVERGENCE ORDER METHODS FOR SOLVING EQUATIONS
Ioannis K. Argyros iargyros@cameron.edu
Santhosh George sgeorge@nitk.edu.in

2020 Mathematics Subject Classification: 65H10, 47H17, 49M15, 65D10, 65G99.
Key words: multi step method, local convergence, Fréchet derivative, system of equations, Banach space.

The local convergence analysis of iterative methods is important since it indicates the degree of difficulty for choosing initial points. In the present study we introduce generalized multi-step high order methods for solving nonlinear equations. The local convergence analysis is given using hypotheses only on the first derivative which actually appears in the methods in contrast to earlier works using hypotheses on higher derivatives. This way we extend the applicability of these methods. The analysis includes computable radius of convergence as well as error bounds based on Lipschitz-type conditions not given in earlier studies. Numerical examples conclude this study.

ON SOME UNIQUE FIXED POINT THEOREMS WITH RATIONAL EXPRESSIONS IN PARTIALLY ORDERED METRIC SPACES
N. Seshagiri Rao seshu.namana@gmail.com
K. Kalyani kalyani.namana@gmail.com

2020 Mathematics Subject Classification: Primary: 54H25, Secondary: 47H10.
Key words: Partially ordered metric spaces, generalized rational contractions, fixed point.

The aim of this paper is to establish some fixed point results of a self mapping satisfying generalized rational contraction conditions in a metric space endowed with a partial order. These results generalized and widen the result of Sharma and Yuel from metrical space to partially ordered metric space and also a few well known results in an ordered metric space. Some examples are illustrated to support the usability of the presented results.

2020 Mathematics Subject Classification: Primary 05C15; Secondary 05B45, 52C22.
Key words: Clique number, chromatic number, maximum clique, greedy coloring, clique number estimates.

We will describe an algorithm to establish an upper estimate of the clique number of a given graph. The procedure is based on greedy legal coloring of the nodes. In order to assess the performance of the procedure we carried out a large scale numerical experiment.

SOME PROPERTIES OF THE GENERALIZED SUBCLASSES OF JANOWSKI TYPE ALPHA-QUASI-CONVEX FUNCTIONS
Gagandeep Singh kamboj.gagandeep@yahoo.in
Gurcharanjit Singh dhillongs82@yahoo.com

2020 Mathematics Subject Classification: 30C45, 30C50.
Key words: Univalent functions, analytic functions, subordination, starlike functions, convex functions, quasi-convex functions, alpha-quasi-convex functions.

The present paper is concerned with certain generalized subclasses of alpha-quasi-convex functions in the open unit disc E={z : |z| < 1}. We establish some properties such as the coefficient estimates, distortion theorems, growth theorems and radius of quasi convexity for these classes. Various earlier known results will follow as special cases.

η-RICCI SOLITONS ON (LCS)_n-MANIFOLDS ADMITTING DIFFERENT SEMI-SYMMETRIC STRUCTURES
Kanak Kanti Baishya kanakkanti.kc@gmail.com
Ashis Biswas biswasashis9065@gmail.com
Adara M. Blaga adarablaga@yahoo.com

2020 Mathematics Subject Classification: 53C15, 53C25.
Key words: η-Ricci soliton, (LCS)_n-manifold, semi-symmetric structure, η-Einstein manifold.

The object of the present paper is to study η-Ricci solitons and Ricci solitons on (LCS)_n-manifolds admitting different equivalency group or class of semi-symmetric conditions based on Kundu and Shaikh [On equivalency of various geometric structures. J. Geom. 105 (2014), 139−165].

TOPOLOGICAL RADICALS OF SEMICROSSED PRODUCTS
Gavriil Andreolas gandreolas@aegean.gr
Michalis Anoussis mano@aegean.gr
Charalampos Magiatis chmagiatis@aegean.gr

2020 Mathematics Subject Classification: Primary 47L65; Secondary 16Nxx.
Key words: Semicrossed products, non-selfadjoint operator algebras, topological radicals, hypocompact radical, scattered radical, dynamical system.

We characterize the hypocompact radical of a semicrossed product in terms of properties of the dynamical system. We show that an element A of a semicrossed product is in the hypocompact radical if and only if the Fourier coefficients of A vanish on the closure of the recurrent points and the 0-Fourier coefficient vanishes also on the largest perfect subset of X.