Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation
Abstract We establish some fixed point theorems by introducing two new classes of contractive mappings in Menger PM-spaces. First, we prove our results for an α - ψ -type contractive mapping and then for a generalized β -type contractive mapping. Some examples and an application to Volterra type integral equation are given to support the obtained results.
Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation
Abstract In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.
Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces
We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.
Some coincidence and periodic points results in a metric space endowed with a graph and applications
The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.
Common fixed point theorems for mappings satisfying common property (E.A.) in symmetric spaces
In this paper, common fixed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.). In the process, a host of previously known results are improved and generalized. We also derive results on common fixed point in probabilistic symmetric spaces.
Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces
In this paper, we introduce cyclic weak $\phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.
(φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces
The purpose of this paper is to extend the notion of (phi,psi)-weak contraction to intuitionistic fuzzy metric spaces, by using an altering distance function. We obtain common fixed point results in intuitionistic fuzzy metric spaces, which generalize several known results from the literature.
Some new fixed point theorems in fuzzy metric spaces
Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of alpha-phi -fuzzy contractive mapping and beta-psi-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.
Further generalization of fixed point theorems in Menger PM-spaces
In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the problem of existence of a fixed point for generalized type contractive mappings in M-complete Menger PM-spaces under arbitrary t-norm. Some examples are furnished to demonstrate the validity of the obtained results.