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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, the concept of perturbed metric was introduced within the metric spaces and some fixed point results were established for self-mappings satisfying such contractive conditions, using Picard operators technique and generalized contractions. Moreover, some applications of the main result to continuous data dependence of the fixed points of Picard operators defined on these spaces were presented. Also, the main result of this paper was applied to study the existence and uniqueness of the solution for an integral equation which models an epidemiological problem. [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]

In this paper, we study the M-iteration process in hyperbolic spaces and prove some strong and Δ-convergence theorems of this iteration process for generalized nonexpansive mappings. Moreover, we establish the weak w²-stability and data dependence theorems for a class of contractive-type mappings by using M-iteration process. The results presented here extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, some existence results for a system of operator inclusions are presented. Qualitative properties of the solution set are also discussed. The method is based on the application of a fixed point theorem for an appropriate operator on the Cartesian product of the given spaces. The approach is new even for the case of the metric spaces. As an application, an existence result for a mixed boundary and initial value problem for a system of second order differential inclusions is given. [ABSTRACT FROM AUTHOR]