The Cigler simple derivation of the q-Carlitz-Dobinski formula is recalled and it is noticed that the formula may be interpreted as the average of powers of random variable X q with the q-Poisson distribution. In parallel new q-Cigler-Dobinski and psi-Carlitz-Dobinski formulas are introduced. At first let us anticipate with ψ-remark. ψ denotes an extension of 1 n! n≥0 sequence to quite arbitrar...

The main purpose of this paper is to study the approximate best proximity pair of cyclic maps and their diameter in fuzzy normed spaces defined by Bag and Samanta. First, approximate best point proximity points on fuzzy normed linear spaces are defined and four general lemmas are given regarding approximate fixed point and approximate best proximity pair of cyclic maps on fuzzy normed spaces. U...

In this study, we present a more general class of rational-type contractions in the domain Hilbert spaces, along with novel coupled implicit relation. We develop several intriguing results and consequences for existence unique fixed points. Further, investigate necessary condition that guarantees well-posedness fixed-point problem self-mappings spaces. Some new observations proposed research br...