Dejan Ilić

QUASI-CONTRACTION ON A CONE METRIC SPACE

In this work we define and study quasi-contraction on a cone metric space. For such a mapping we prove a fixed point theorem. Among other things, we generalize a recent result of H. L. Guang and Z. Xian, and the main result of Ciric is also recovered.

Some new extensions of Banach’s contraction principle to partial metric space☆

Abstract In S.G. Matthews [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183–197], the author introduced and studied the concept of partial metric space, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this work we study fixed point results for new extensions of Banach’s contraction principle to partial metric space, and we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

Extensions of the Zamfirescu theorem to partial metric spaces

Abstract Zamfirescu [T. ZamfirescuFix point theorems in metric spaces Arch. Math. (Basel) 23 (1972) 292-298], obtained a very interesting fixed point theorem on complete metric spaces by combining the results of S. Banach, R. Kannan and S.K. Chatterjea. In [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we study new extensions of the Zamfirescu theorem to the context of partial metric spaces, and among other things, we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

One linear analytic approximation for stochastic integrodifferential equations

Abstract This article concerns the construction of approximate solutions for a general stochastic integrodifferential equation which is not explicitly solvable and whose coefficients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the L p -th norm, uniformly on the time interval. The convergence with probability one is also given.

Common fixed points for maps on metric space with w-distance

Abstract The purpose of this paper is to generalize and to unify fixed point theorems of Das and Naik, Ciric, Jungck and Ume in terms of a w -distance on complete metric space.

Coupled Coincidence Point and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces with -Distance

We introduce the concept of a -compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with -distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend, and unify several well-known comparable results in the literature.

On Ćirić maps with a generalized contractive iterate at a point and Fisher's quasi-contractions in cone metric spaces

In this paper, we generalize and unify some results of Sehgal and Guseman, and Cirics theorem for mappings with a generalized contractive iterate at a point to cone metric spaces, in which the cone does not need to be normal. As corollaries, we obtain recent results of Huang and Zhang, and Raja and Vaezpour. Furthermore, we introduce the definition of Fisher quasi-contractions on cone metric spaces and study their properties. Among other things, using new method of proof, we solve the open problem for the interval of contractive constant @l of (Ciric) quasi-contraction in non-normal cone metric spaces, and as sn immediate corollary, we recover the recent result of Rezapour and Hamlbarani.

Three extensions of Ćirić quasicontraction on partial metric spaces

In this paper we define and study three extensions of the notion of Ćirić quasicontraction to the context of partial metric spaces. For such mappings, we prove fixed point theorems. Among other things, we generalize a recent result of Altun, Sola and Simsek, of Ilić et al., of Matthews, and the main result of Ćirić is also recovered. The theory is illustrated by some examples.MSC:15A09, 15A24.

Fixed points of mappings with a contractive iterate at a point in partial metric spaces

In 1994, Matthews introduced and studied the concept of partial metric space and obtained a Banach-type fixed point theorem on complete partial metric spaces. In this paper we study fixed point results of new mappings with a contractive iterate at a point in partial metric spaces. Our results generalize and unify some results of Sehgal, Guseman and Ćirić for mappings with a generalized contractive iterate at a point to partial metric spaces. We give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples.

Hybridization of accelerated gradient descent method

We present a gradient descent algorithm with a line search procedure for solving unconstrained optimization problems which is defined as a result of applying Picard-Mann hybrid iterative process on accelerated gradient descent SM method described in Stanimirović and Miladinović (Numer. Algor. 54, 503–520, 2010). Using merged features of both analyzed models, we show that new accelerated gradient descent model converges linearly and faster then the starting SM method which is confirmed trough displayed numerical test results. Three main properties are tested: number of iterations, CPU time and number of function evaluations. The efficiency of the proposed iteration is examined for the several values of the correction parameter introduced in Khan (2013).