Sumit Chandok

Fixed point theorem for weakly Chatterjea-type cyclic contractions

In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and derive the existence of a fixed point for such mappings in the setup of complete metric spaces. Our result extends and improves some fixed point theorems in the literature. Example is given to support the usability of the result.MSC:41A50, 47H10, 54H25.

Some common fixed point theorems for generalized nonlinear contractive mappings

Sufficient conditions for the existence of a common fixed point for generalized nonlinear contractive mappings are derived. As applications, some results on the set of best approximation for this class of mappings are also obtained. The proved results generalize and extend various known results in the literature.

Some coupled common fixed points for a pair of mappings in partially ordered G-metric spaces

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed g-monotone property in partially ordered G-metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature. To illustrate our results, we give some examples.

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Sufficient conditions for the existence of a common fixed point of generalized -weakly contractive noncommuting mappings are derived. As applications, some results on the set of best approximation for this class of mappings are obtained. The proved results generalize and extend various known results in the literature.

Some Common Fixed Point Results for Rational Type Contraction Mappings in Complex Valued Metric Spaces

We prove some common fixed point theorems for two pairs of weakly compatible mappings satisfying a rational type contractive condition in the framework of complex valued metric spaces. The proved results generalize and extend some of the known results in the literature.

Fixed point theorems on b-metric spaces for weak contractions with auxiliary functions

In this paper, we obtain some fixed point results for generalized weakly contractive mappings with some auxiliary functions in the framework of b-metric spaces. The proved results generalize and extend the corresponding well-known results of the literature. Some examples are also provided in order to show that these results are more general than the well-known results existing in literature.MSC:47H10, 54H25.

Optimal solutions for nonlinear proximal C N -contraction mapping in metric space

The objective of this paper is to solve an optimal solutions for new nonlinear mapping in the setting of metric spaces. Our results extend, generalize, and improve some known results from best proximity point theory and fixed point theory. Examples are given to support our main results.MSC:41A50, 47H10, 54H25.

Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem

In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive several corollaries of our main theorems. As application, we establish an existence result for a two-point boundary value problem of second order differential equation.

Coupled common fixed point theorems for generalized nonlinear contraction mappings with the mixed monotone property in partially ordered metric spaces

The purpose of this paper is to establish some coupled coincidence point theorems for generalized nonlinear contraction mappings with the mixed g-monotone property in the framework of metric spaces endowed with partial order. The theorems presented in this paper are generalizations and improvements of the several well-known results in the literature.MSC:46N40, 47H10, 54H25, 46T99.

Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation

Abstract. We prove some new results on the existence of common fixed points for nonexpansive and asymptotically nonexpansive mappings in the framework of convex metric spaces. We also obtain some results on common fixed points from the set of best and best simultaneous approximations as applications. The proved results generalize and extend some of the known results in the literature.