Related papers: On a Generalized Briot-Bouquet type Differential S…
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller C^k_pi maps f_i:E sqcap F_i to F_i with F_i Banach and F=projlim F_i .…
Motivated by the work of Prajapati \emph{et al.} \cite{PAA}, here we study some explicit form of the generalized Laguerre polynomials $L_{\lfloor\frac{n}{q}\rfloor}^{(\alpha,\beta)}(z)$, when $q=1$.
Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…
In this article we study the differentiability of Mather's $\beta$-function on closed surfaces and its relation to the integrability of the system.
Starting from the Colombeau's full generalized functions, the sharp topologies and the notion of generalized points, we introduce a new kind differential calculus (for functions between totally disconnected spaces). We study generalized…
In this paper, subordination results are studied for certain subclass of p-valent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclass under investigation is defined by using certain new…
We prove optimal ${L}^2$ bounds for a pair of Hilbert space valued differentially subordinate martingales under a change of law. The change of law is given by a process called a weight and sharpness in this context refers to the optimal…
G.D. Birkhoff extended the classical Riemann-Hilbert problem for differential equations to the case of ``fuchsian'' linear $q$-difference systems with rational coefficients. He solved it in the generic case: the classifying object which he…
In this paper, we establish a fundamental inequality for fourth order partial differential operator $\cal P=\alpha\partial_s+\beta\partial_{ss}+\Delta^2$ ($\alpha, \beta\in\mathbb{R}$) with an abstract exponential-type weight function. Such…
In this work, the subclass of the function class S of bi-univalent functions associated with the quasi-subordination is defined and studied. Also some relevant classes are recognized and connections to previus results are made.
In this article, we study the Bohr operator for the operator valued subordination class $S(f)$ consisting of holomorphic functions subordinate to $f$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$, where $f:\mathbb{D}…
In the paper, we have shown that every entire solution of the differential difference equation $\Delta_{\eta}^{m}f-Q_1=(\Delta_{\eta}^{k}f-Q_{2})e^{P}$ satisfy hyper order of $f=$degree of $P$ and using this result we prove differential…
In this paper, the derivative tent space \(DT_p^q(\alpha)\) is introduced. Then, we study \(\mathcal{C}_{\mathcal{B}_{{\log}^\gamma}^\beta}(DT_p^q(\alpha)\cap\mathcal{B}_{{\log}^\gamma}^\beta)\), the closure of the derivative tent space…
Theory of differential subordination provides techniques to reduce differential subordination problems into verifying some simple algebraic condition called admissibility condition. We exploit the first order differential subordination…
In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq…
We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these…
Using simple operator-valued analytic function considerations several general analytic subordination results for a freely Markovian triple of operator algebras are derived from the analytic subordination result for generalized resolvents in…
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of {\em Colombeau type} in the sense that it contains a copy of the space of Schwartz…
This work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze scalar products of off-shell Bethe states…
In this paper, we employ a novel second and third-order differential subordination technique to establish the sufficient conditions for functions to belong to the classes $\mathcal{S}^*_s$ and $\mathcal{S}^*_{\rho}$, where $\mathcal{S}^*_s$…