A class of generalized $(\psi ,\alpha ,\beta )$ —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.

An analysis was carried out to investigate the time period of the thermally induced vibration of clamped and simply supported circular plates with circular variation both in thickness and density. Prior to this study, the variations considered were either linear, quadratic, parabolic, or exponential in nature. To study thermal effect, one-dimensional linear temperature variation on the plates is taken into consideration. Rayleigh–Ritz method is applied to compute the time period of the first three modes of vibration for both plates by varying tapering parameter, thermal gradient, and density. Convergence study of frequency modes for both plates conducted suggests that the convergence rate in case of circular variation is faster than the other studies done. A comparison of time period with the available published results is done. The comparison done concludes that time period obtained in the present study by varying thermal gradient and tapering parameter is found to be less than the other studies done for the same set of parameters. This study helped to establish the fact that, by using circular variation in plate parameters, we can get less time period of frequency modes in comparison to other variations considered till date.

In this article, generalized C Ψ β - rational contraction is defined and the existence and uniqueness of fixed points for self map in partially ordered metric spaces are discussed. As an application, we apply our result to find existence and uniqueness of solutions of second order differential equations with boundary conditions.

The purpose of this paper is to obtain some results on existence of fixed points for contractive mappings in fuzzy metric spaces using control function. We prove our results on fuzzy metric spaces in the sense of George and Veeramani. Our results mainly generalize and extend the result of Grabeic (1988). As an application, a consequence theorem of integral type contraction is given in support of our result