Miloje Rajović

Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces

A concept of -monotone mapping is introduced, and some fixed and common fixed point theorems for -non-decreasing generalized nonlinear contractions in partially ordered complete metric spaces are proved. Presented theorems are generalizations of very recent fixed point theorems due to Agarwal et al. (2008).

Common fixed-point results for nonlinear contractions in ordered partial metric spaces

In this paper, a new class of a pair of generalized nonlinear contractions on partially ordered partial metric spaces is introduced, and some coincidence and common fixed-point theorems for these contractions are proved. Presented theorems are twofold generalizations of very recent fixed-point theorems of Altun and Erduran (Fixed Point Theory Appl 2011(Article ID 508730):10, 2011), Altun et al. (Topol Appl 157(18):2778-2785, 2010), Matthews (Proceedings of the 8th summer conference on general topology and applications, New York Academy of Sciences, New York, pp. 183-197, 1994) and many other known corresponding theorems.2000 Mathematics Subject Classifications: 54H25; 47H10.

Remarks on Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings

Recently, Jose R. Morales and Edixon Rojas [Jose R. Morales and Edixon Rojas, Cone metric spaces and fixed point theorems of T-Kannan contractive mappings, Int. J. Math. Anal. 4 (4) (2010) 175-184] proved fixed point theorems for T-Kannan and T-Chatterjea contractions in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this without using the normality condition. Two results for these classes of contractive mappings are also proved. Examples are given to illustrate the results.

On Mann implicit iterations for strongly accretive and strongly pseudo-contractive mappings

Abstract For a Lipschitz strongly accretive map considered by Chidume in [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint No. IC2000098; C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear analysis and applications: to V. Lakshmikantam on his 80th birthday, vols. 1 and 2, Kluwer Acad. Publ., Dordrecht, 2003, pp. 383–429], it is known that a classical Picard-type iteration process converges strongly to a zero of the operator. He also proved that the rate of convergence, in this case, is at least as fast as a geometric progression. In this paper we study the Mann implicit iteration sequence for strongly accretive and strongly pseudo-contractive mappings. We showed that this implicit scheme gives better convergence rate estimate. Presented results improve the corresponding results of [C.E. Chidume, Picard iteration for strongly accretive and strongly pseudo-contractive Lipschitz maps, ICTP Preprint No. IC2000098; C.E. Chidume, Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear analysis and applications: to V. Lakshmikantam on his 80th birthday, vols. 1 and 2, Kluwer Acad. Publ., Dordrecht, 2003, pp. 383–429; L. Liu, Approximation of fixed points of a strictly pseudo-contractive mapping, Proc. Am. Math. Soc. 125 (2) (1997) 1363–1366; W.R. Sastry, G.V.R. Babu, Approximation of fixed points of strictly pseudo-contractive mappings on arbitrary closed, convex sets in a Banach space, Proc. Amer. Math. Soc. 128 (2000) 2907–2909; Y. Song, R. Chen, Viscosity approximative methods to Cesaro means for non-expansive mappings, Appl. Math. Comput. 186 (2) (2007) 1120–1128].

Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics

Abstract In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived.

Common fixed point theorems for non-self-mappings in metric spaces of hyperbolic type

In this paper, the concept of a pair of non-linear contraction type mappings in a metric space of hyperbolic type is introduced and the conditions guaranteeing the existence of a common fixed point for such non-linear contractions are established. Presented results generalize and improve some of the known results. An example is constructed to show that our theorems are genuine generalizations of the main theorems of Assad, Ciric, Khan et al., Rhoades and Imdad and Kumar. One of the possible applications of our results is also presented.

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.

Transformation of linear non-homogeneous differential equations of the second order to homogeneous

The main results of this paper give a negative answer to the problem of transformations of the linear non-homogeneous differential equations of order two into a homogeneous one, by means of the internal elements of the non-homogeneous equation. Other results, concerning perturbation by means of a sum with a certain mapping z and the exploitation of the methods are presented.

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 .

Perturbation of solutions of ordinary linear homogeneous differential equations of the second order

In this paper we give a method for peturbation of solutions of linear homogeneous differential equation of the second order.