On locally bounded spaces and their products

In this paper we present a new characterization of locally bounded topological vector spaces, which generalize earlier characterizations of Aoki [1] and Rolewicz [13]. Further we shall prove that Topological vector space is Φ-paranormable (class introduced by S. Kasahara in 1973) if and only if it is a product of locally bounded spaces

On locally bounded spaces and their products

In this paper we present a new characterization of locally bounded topological vector spaces, which generalize earlier characterizations of Aoki [1] and Rolewicz [13]. Further we shall prove that Topological vector space is Φ-paranormable (class introduced by S. Kasahara in 1973) if and only if it is a product of locally bounded spaces

Some new results on a linear equation of the second order

AbstractWork on solving the second order linear oscillation defined by Eq. (1.1), with continuous and positive coefficient Φ(x) that satisfies Lipschitz’s condition on semi-axis [0,+∞) and the divergence of ∫0+∞(Φ−G′2)dx, had started since the 1830s with Sturm’s theorems. This paper presents generalizations as well as a simplification of classical Sturm’s theorems on the location and the position of zero oscillations, which have not been included in Amrein et al. (2005) [5]. Besides, according to results from Dimitrovski and Mijatović (1997) [1], Dimitrovski et al. (2007) [2] and Dimitrovski et al. (2007) [4], we add some ideas and supplements (Theorems 2.4–2.8, 2.10 and 2.11) to the classical Sturm’s theory of oscillations

The number of zero solutions for complex canonical differential equation of second order with constant coefficients in the first quadrant

The study of complex differential equations in recent years has opened up some of questions concerning the determination of the frequency of zero solutions, the distribution of zero, oscillation of the solution, asymptotic behavior, rank growth and so on. Besides, this is solved by only some classes of differential equations. In this paper, our aim was to determine the number of zeros and their arrangement in the first quadrant, for the complex canonical differential equation of the second order. The accuracy of our results, we illustrate with two examples

On nonlinear quasi-contractions

Lj. Ciric [2] first introduced the notion of quasi - contractions and proved the fixed point theorem for this class of mappings. Ciri'c's result was extended to nonlinear quasi - contractions by A. A. Ivanov [4]. In this paper we present new generalizations of Ivanov's fixed point theorem

On the convergence of Ishikawa iterates defined by nonlinear quasi-contractions

In [8] Lj. B. Ćirić proved general result on the convergence of Ishikawa iterates of nonlinear quasi - contractions defined on Takahashi convex metric space. In this paper we present two generalizations of Ćirić's result

On nonlinear quasi-contractions

Lj. Ciric [2] first introduced the notion of quasi - contractions and proved the fixed point theorem for this class of mappings. Ciri'c's result was extended to nonlinear quasi - contractions by A. A. Ivanov [4]. In this paper we present new generalizations of Ivanov's fixed point theorem

On the convergence of Ishikawa iterates defined by nonlinear quasi-contractions

In [8] Lj. B. Ćirić proved general result on the convergence of Ishikawa iterates of nonlinear quasi - contractions defined on Takahashi convex metric space. In this paper we present two generalizations of Ćirić's result

Coupled coincidence points for two mappings in metric spaces and cone metric spaces

This article is concerned with coupled coincidence points and common fixed points for two mappings in metric spaces and cone metric spaces. We first establish a coupled coincidence point theorem for two mappings and a common fixed point theorem for two w-compatible mappings in metric spaces. Then, by using a scalarization method, we extend our main theorems to cone metric spaces. Our results generalize and complement several earlier results in the literature. Especially, our main results complement a very recent result due to Abbas et al. © 2012 Long et al; licensee Springer

Some coincidence point results for generalized (ψ,φ)-weakly contractions in ordered b-metric spaces

© 2015, Roshan et al.; licensee Springer. In this paper we present some coincidence point results for four mappings satisfying generalized (ψ,φ)-weakly contractive condition in the framework of ordered b-metric spaces. Our results extend, generalize, unify, enrich, and complement recently results of Nashine and Samet (Nonlinear Anal. 74:2201-2209, 2011) and Shatanawi and Samet (Comput. Math. Appl. 62:3204-3214, 2011). As an application of our results, periodic points of weakly contractive mappings are obtained. Also, an example is given to support our results