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In this paper we give some fixed point theorems for nonself generalized contractions on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. S¸erban (I.A. Rus, M.-A. S¸erban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273) in complete metric spaces. We prove our results without using the completeness of the metric structure. [ABSTRACT FROM AUTHOR]

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X; d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of Ulam stability of fixed point equation with respected to a directed graph. Two fixed point theorems of Matkowski and of Jachymski are discussed further in the sense of this stability concept. Some examples about the validity of our notion are given. Finally, we discuss the vagueness of the recent stability results of Sintunavarat [Sintunavarat, W., A new approach to α-ψ -contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadowing results, Carpathian J. Math., 31 (2015), 395-401]. [ABSTRACT FROM AUTHOR]