Abstract. We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms. Thanks to this connection, we then show that certain ratios of probabilities are specializations of the Rogers-Ramanujan, and RamanujanSelbergGordon-Göllnitz continued fractions. One particular evaluation depend...

Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G V c|x|−2 in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), C1(RN, RN), 0 ≤ C1(RN) and c > 0. The proofs are carried out an application L2-weighted Hardy inequality bilinear form techniques.

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

The concept of symmetry is a very vast topic that involved in the studies several phenomena. This enables us to discuss phenomenon some systematic pattern depending upon type phenomenon. Each has its own symmetry. used discussion this article symmetric distance-measuring function. presents notions abstract interpolative Reich-Rus-Ćirić-type contractions with shrink map and examines existence ϕ-...

in this paper,  we provide two different kinds of fixed pointtheorems in  fuzzy metric spaces. the first kind is for the fuzzy$varepsilon$-contractive type mappings and  the second kind is forthe fuzzy order $psi$-contractive type mappings. they improve thecorresponding  conclusions in the literature.

In this paper, we study composition operators Cφf = f ◦ φ, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

Abstract We utilize Hardy-Rogers contraction and CJM−contraction in a C * −algebra valued partial metric space to create an environment establish fixed point. Next, we present examples elaborate on the novel validate our result. conclude paper by solving boundary value problem matrix equation as applications of main results which demonstrate significance motivation for such investigations.

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractiv...