Renu Chugh

Common fixed points for weakly compatible maps

The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalizes the results of Jungck [3], Fisher [1], Kang and Kim [8], Jachymski [2], and Rhoades [9].

Property in -Metric Spaces

We prove two general fixed theorems for maps in -metric spaces and then show that these maps satisfy property .

On the Rate of Convergence of Kirk-Type Iterative Schemes

The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C

General Common Fixed Point Theorems and Applications

The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đoric and Lazovic (2011) for a multivalued map on a metric space satisfying Ciric-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ciric (1974). Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed.

Common Fixed Point Results in G-Metric Spaces and Applications

common fixed point theorem using EA-property for four weakly compatible maps is obtained in the setting of G- metric spaces without exploiting the notion of continuity. Our results generalize the results of Abbas and Rhoades(7), and Manro et. al.(11). Moreover, we show that these maps satisfy property R. Applications to certain intergral equations and functional equations are also obtained.

Convergence of SP iterative scheme with mixed errors for accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach spaces

In this paper, we study the strong convergence of SP iterative scheme with mixed errors for the accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach spaces. We show that this iterative scheme is almost stable for both types of operators. Moreover, with the help of computer programs in C++, comparison between SP, Ishikawa and Noor iterative schemes with errors is also shown for both types of operators through examples.

Julia sets and Mandelbrot sets in Noor orbit

In recent literature, researchers have generated Julia sets and Mandelbrot sets in Mann and Ishikawa orbits that are examples of two-step and three-step feedback processes respectively. This paper presents further generalization of Julia and Mandelbrot sets for complex-valued polynomials such as quadratic, cubic and higher degree polynomials using a Noor orbit, which is a four-step iterative procedure. The graphical images of Julia and Mandelbrot sets have been visualized and certain patterns in Mandelbrot sets have been recognized. It is fascinating to see that a few Mandelbrot sets are akin to a butterfly or a coupled urn or a coupled trident.

Suzuki-Type Fixed Point Results in G-Metric Spaces and Applications

paper, we obtain some Suzuki-type fixed point results in G-metric spaces and as well as discuss the G-continuity of the fixed point. The direction of our extension/generalization is new and very simple. An illustrative example is also given to show that our main result is extension of the existing ones. Moreover, we show that these maps satisfy property P. Application to certain class of functional equations arising in dynamical programming is also obtained.

Properties P and Q for Suzuki-type fixed point theorems in metric spaces

The aim of this paper is to present several results for maps defined on a metric space involving contractive conditions of Suzuki-type which satisfy properties P and Q. An interesting fact about this study is that none of these maps has any nontrivial periodic points.

SOME STRONG CONVERGENCE RESULTS OF RANDOM ITERATIVE ALGORITHMS WITH ERRORS IN BANACH SPACES

In this paper, we study the strong convergence and stability of a new two step random iterative scheme with errors for accretive Lipschitzian mapping in real Banach spaces. The new iterative scheme is more acceptable because of much better convergence rate and less restrictions on parameters as compared to random Ishikawa iterative scheme with errors. We support our analytic proofs by providing numerical examples. Applications of random iterative schemes with errors to variational inequality are also given. Our results improve and establish random generalization of results obtained by Chang [4], Zhang [31] and many others.