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We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, and Piri and Kumam in Fixed Point Theory Appl. 2014:210, , etc.). Examples are provided to support the usability of our results. [ABSTRACT FROM AUTHOR]

It is well known that the concept of a best proximity point includes that of a fixed point as a special case. In this paper, we show that the best proximity point theorems of Basha and Shahzad (Fixed Point Theory Appl. 2012:42, ) and of Fernández-León (J. Nonlinear Convex Anal. 15(2):313-324, ) can be regarded as a fixed point theorem for multivalued mappings which is modified as regards the results of Mizoguchi and Takahashi (J. Math. Anal. Appl. 141(1):177-188, ) and of Kada et al. (Math. Jpn. 44(2):381-391, ). [ABSTRACT FROM AUTHOR]

It is well known that the concept of a best proximity point includes that of a fixed point as a special case. In this paper, we show that the best proximity point theorems of Basha and Shahzad (Fixed Point Theory Appl. 2012:42, ) and of Fernández-León (J. Nonlinear Convex Anal. 15(2):313-324, ) can be regarded as a fixed point theorem for multivalued mappings which is modified as regards the results of Mizoguchi and Takahashi (J. Math. Anal. Appl. 141(1):177-188, ) and of Kada et al. (Math. Jpn. 44(2):381-391, ). [ABSTRACT FROM AUTHOR]

In this paper, owing to the concept of F-contraction, we define two new classes of functions $M(S,T)$ and $N(S,T)$, and we prove some new fixed point results for single-valued and multivalued mappings in complete metric spaces. Our results extend, generalize and unify several known results in the literature. We include an example to show that the generalization is proper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of $(\alpha,\psi)$-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries. [ABSTRACT FROM AUTHOR]

We study self-mappings on complete metric spaces, which we refer to as higher-order Lipschitz mappings. These mappings generalise Lipschitz mappings, the latter which are equivalent to first-order Lipschitz mappings studied in this paper. The main result of this paper is to extend the Banach fixed point theorem (and an often-cited generalisation) to higher-order contraction mappings. We also present results on the problem of local Lipschitzity of these higher-order Lipschitz mappings. [ABSTRACT FROM AUTHOR]

In this paper, we show that some examples in (Mursaleen et al. in Fixed Point Theory Appl. 2012:124, 2012) are not correct. Then, we extend, improve and generalize their results. Finally, we state some examples to illustrate our obtained results. MSC: 47H10, 54H25. [ABSTRACT FROM AUTHOR]