Abstract: Some characterizations of boundedness in and will be described, where denote the Smirnov class and the Privalov class on the upper half plane , respectively. PubDate: Tue, 19 Dec 2017 08:41:28 +000

Abstract: We investigate the structure of symmetric solutions of the matrix equation , where and are -by- matrices over a principal ideal domain and is unknown -by- matrix over . We prove that matrix equation over has a symmetric solution if and only if equation has a solution over and the matrix is symmetric. If symmetric solution exists we propose the method for its construction. PubDate: Sun, 05 Nov 2017 08:14:27 +000

Abstract: We consider the problem of determining whether two polynomial matrices can be transformed to one another by left multiplying with some nonsingular numerical matrix and right multiplying by some invertible polynomial matrix. Thus the equivalence relation arises. This equivalence relation is known as semiscalar equivalence. Large difficulties in this problem arise already for 2-by-2 matrices. In this paper the semiscalar equivalence of polynomial matrices of second order is investigated. In particular, necessary and sufficient conditions are found for two matrices of second order being semiscalarly equivalent. The main result is stated in terms of determinants of Toeplitz matrices. PubDate: Thu, 26 Oct 2017 00:00:00 +000

Abstract: The aim of this paper is to present a new improved semilocal and local convergence analysis for two-step secant method to approximate a locally unique solution of a nonlinear equation in Banach spaces. This study is important because starting points play an important role in the convergence of an iterative method. We have used a combination of Lipschitz and center-Lipschitz conditions on the Fréchet derivative instead of only Lipschitz condition. A comparison is established on different types of center conditions and the influence of our approach is shown through the numerical examples. In comparison to some earlier study, it gives an improved domain of convergence along with the precise error bounds. Finally, some numerical examples including nonlinear elliptic differential equations and integral equations validate the efficacy of our approach. PubDate: Sun, 24 Sep 2017 00:00:00 +000

Abstract: We introduce the concept of -distance (an analogue of -metric), -proximal contraction, and -proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results. PubDate: Wed, 26 Apr 2017 00:00:00 +000

Abstract: The purpose of this paper is to introduce new concepts of -admissible Geraghty type generalized -contraction and to prove that some fixed point results for such mappings are in the perspective of partial -metric space. As an application, we inaugurate new fixed point results for Geraghty type generalized graphic -contraction defined on partial metric space endowed with a directed graph. On the other hand, one more application to the existence and uniqueness of a solution for the first-order periodic boundary value problem is also provided. Our findings encompass various generalizations of the Banach contraction principle on metric space, partial metric space, and partial -metric space. Moreover, some examples are presented to illustrate the usability of the new theory. PubDate: Wed, 15 Mar 2017 00:00:00 +000

Abstract: For Banach algebras and , we show that if is unital and commutative, each bi-Jordan homomorphism from into a semisimple commutative Banach algebra is a bihomomorphism. PubDate: Tue, 31 Jan 2017 00:00:00 +000