In this article, we introduce a new concept of contraction called F-Khan-contractions and prove a fixed point theorem concerning this contraction which generalizes the results announced by Khan [M. S. Khan, Rend.

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In this paper, we study some results of existence and uniqueness of fixed points for a class of mappings satisfying an inequality of rational expressions. Our main result extends and unifies the well-known results of Khan [M. S. Khan, Rend. Inst. Math. Univ. Trieste, 8 (1976), 69-72].

In this paper, we introduce the concept of generalized asymmetric metric spaces and we prove some fixed point theorems in the setting of this metric spaces and also some illustrative examples are given. The presented results generalize and improve several results of the topics in the literature.

Existence and uniqueness of fixed points are established for a mapping satisfying a new type of contractive condition involving a rational expression on a generalized metric space. Some main results by Ahmad et al. [J. Ahmad, M. Arshad, C. Vetro, Int. J. Anal., 2013 (2013), 6 pages] are extended and generalized, also several particular cases and an illustrative example are given. c 2016 All rights reserved.

In this paper, we introduce the notion of an F-contraction in the setting of complete asymmetric metric spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature.

Letestablished under which the operator preserves an almost spirallike mapping of type β and order α and spirallike mapping of type β and order α , respectively. In particular, our results reduce to many well-known results.Keywords: Roper-Suffridge extension operator, Reinhardt Domain, Almost spirallike mapping of type β and order α , Spirallike mapping of type β and order α , Minkowski functional.

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