Fixed points of generalized cyclic contractions without continuity and application to fractal generation

In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces

Cyclic Type Fixed Point Results in 2-Menger Spaces

summary:In this paper we introduce generalized cyclic contractions through $r$ number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type $t$-norm. In another theorem we use a control function with minimum $t$-norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples

Determining Fuzzy Distance between Sets by Application of Fixed Point Technique Using Weak Contractions and Fuzzy Geometric Notions

In the present paper, we solve the problem of determining the fuzzy distance between two subsets of a fuzzy metric space. We address the problem by reducing it to the problem of finding an optimal approximate solution of a fixed point equation. This approach is well studied for the corresponding problem in metric spaces and is known as proximity point problem. We employ fuzzy weak contractions for that purpose. Fuzzy weak contraction is a recently introduced concept intermediate to a fuzzy contraction and a fuzzy non-expansive mapping. Fuzzy versions of some geometric properties essentially belonging to Hilbert spaces are considered in the main theorem. We include an illustrative example and two corollaries, one of which comes from a well-known fixed point theorem. The illustrative example shows that the main theorem properly includes its corollaries. The work is in the domain of fuzzy global optimization by use of fixed point methods

Hyers–Ulam–Rassias Stability of Set Valued Additive and Cubic Functional Equations in Several Variables

In this paper, we establish Hyers–Ulam–Rassias stability results belonging to two different set valued functional equations in several variables, namely additive and cubic. The results are obtained in the contexts of Banach spaces. The work is in the domain of set valued analysis