Search

In this paper, we introduce a new class of contractive mapping in intuitionistic fuzzy metric space (IFMS). We establish fixed point theorems under such contractive mapping in complete IFMS and prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in IFMS.

The aim of this paper is to obtain a fixed point theorem for mappings satisfying a generalized ($$\psi , \phi$$)-weak contractive type condition in a complete metric space. Moreover, our result also generalizes some well known theorems in the literature.

We obtain a Meir–Keeler type fixed-point theorem which gives a new solution to the Rhoades’ problem on the existence of contractive mappings that admit discontinuity at the fixed point. Meir–Keeler type solutions of the Rhoades’ problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.

In this paper, a fixed point theorem for multi-valued mappings on a complete metric space is established taking a general contractive condition which generalizes several contractive conditions. Many generalizations of some well known results are also obtained as corollaries. Further, we give an application to the existence and uniqueness of solutions for certain classes of functional equations arising in dynamic programming.