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In this paper existence and uniqueness of fixed points are proved for self maps, satisfying a new contraction without assuming the compatibility and commutative property of maps. Some remarks and applications to integral type contraction are given to illustrate the importance of our results. An open problem for future research is also given.

In this paper, we present some fixed point results satisfying generalized contractive condition with new auxiliary function in complete metric spaces. More precisely, the structure of the paper is the following. In the first section, we present some useful notions and results. The main aim of second section is to establish some new fixed point results in complete metric spaces. Finally, in the third section, we show the validity and superiority of our main results by suitable example. Also, as an application of our main result, some interesting corollaries have been included, which make our concepts and results effective. Our main result generalizes some well known existing results in the literature.

Our aim in this communication is to present a new type of contraction and common fixed point results for non-continuous self mappings without using the compatibility and commutative property. Moreover, we have found common fixed point without using the Cauchy's criterion for convergence. Some illustrative examples with graphical representation and remarks are given to justify that the contraction introduced in the main result is new and unique, which will be useful for future researches.

In this paper, we prove fixed point results employing mixed weakly monotone maps, C-class functions and altering distance function in the framework of S-metric space. Here, integral application has additionally been given.

The aim of this paper is to introduce the concept of cyclic Open image in new window —contraction for coupled maps on generalized fuzzy metric space. After that, some significant results of coupled maps of cyclic contraction mappings have been given on generalized fuzzy metric space. Also, we utilize the thought of continuous mappings, weakly commuting mappings, closed subset and complete subspace for demonstrating results.

A class of generalized ( &psi, &alpha, &beta, ) &mdash, weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

In this paper, we prove a fixed point theorem for contractive mapping of integral type in complete metric spaces by using iterative approximations. This paper extends and improves results of Rakotch 1962, Branciari 2002, and several other results announced by many authors. An example and few remarks are given to show that our result is a proper extension of existing ones.