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We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

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]

Let K:= R or C, 0 < κ < 1 and f ∈ C([0, b] × K³, K). In this paper we use the weakly Picard operator theory technique to study the following functional-differential equation y0(x) = f(x; y(x); y0(x); y(κx)); x ∈ [0, b]. [ABSTRACT FROM AUTHOR]

We introduce the concept of semicompleteness on semimetric space, which is weaker than completeness. We prove fixed point theorems for contractions in semicomplete semimetric spaces. Also, we generalize Jachymski-Matkowski-Świątkowski's fixed point theorem in semimetric spaces. [ABSTRACT FROM AUTHOR]