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In 2000, A. Branciari introduced the concept of $$\nu $$ ν -generalized metric space. In this paper, we find a topology on $$\nu $$ ν -generalized metric spaces (X, d) which fits in X very well.
Some novel convolution properties for meromorphically multivalent functions associated with the generalized Bessel functions of the first kind are derived.
Let $$\mathbb {K}$$ K , $$\mathbb {F}$$ F be two fields of real or complex numbers and X be a normed space over field $$\mathbb {F}$$ F . In this paper, we consider the following generalized logarithmic functional equation: $$\begin{aligned} f(x^a y^b)= Af(x) + Bf(y), \end{aligned}$$ f ( x a y b ) = A f ( x ) + B f ( y ) , where f maps from...
By using a new fractional differintegral operator which was studied in a recent work (Mediterr J Math 13:1535–1553 2016), we first introduce various classes of analytic functions in terms of the subordination and then prove several inclusion results for each of these classes of analytic functions. We also consider some useful special cases and consequences of the results which are presented in this...
Making use of the critical point theory, we obtain the existence of periodic solutions for higher order difference equations containing both many advances and retardations. The main approaches used in our paper are variational techniques and the Saddle Point Theorem. The problem is to solve the existence of periodic solutions for higher order difference equations containing both many advances and...
Analogous to L. Schwartz’ study of the space $$\mathcal {D}'(\mathcal {E})$$ D ′ ( E ) of semi-regular distributions, we investigate the topological properties of the space $$\mathcal {D}'(\dot{\mathcal {B}})$$ D ′ ( B ˙ ) of semi-regular vanishing distributions and give representations of its dual and of the scalar product with this dual. In order to determine...
The aim of this paper is to present fixed point results of Perov type contractive mappings in the framework of cone metric spaces endowed with a graphic structure. Some examples are presented to support the results proved herein. We also provide an example to show that our results are substantial generalization of comparable results in the existing literature. As an application of our results, we...
In this paper, we introduce a modification of the Szász–Mirakjan–Kantorovich operators as well as Stancu operators (or a Dunkl generalization of modified Szász–Mirakjan–Kantrovich operators) which preserve the linearity. This type of modification enables better error estimation on the interval $$[1/2,\infty )$$ [ 1 / 2 , ∞ ) rather than the classical Dunkl Szász–Mirakjan–Kantrovich as...
For $$\mathcal {X}=\left( X_{n}\right) _{n\in \mathbb {N}}$$ X = X n n ∈ N a sequence of Banach spaces and $$1\le p<\infty $$ 1 ≤ p < ∞ , we consider $$l_{p}\left( \mathcal {X} \right) $$ l p X and $$c_{0}\left( \mathcal {X}\right) $$ c 0 X the corresponding vector valued sequence spaces. In this paper we give a complete characterization...
In this paper, we consider the Cauchy problem for the three dimensional chemotaxis–Euler equations. By exploring the new a priori estimates, we prove the global existence of weak solutions for the 3D chemotaxis–Euler equations.
In this paper, we prove the existence of multiple solutions for the following fractional p-Laplacian equation of Schrödinger–Kirchhoff type with sign-changing potential $$\begin{aligned} M\left( \int \int _{{\mathbb {R}}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right) (-\Delta )^s_p u+V(x)|u|^{p-2}u=f(x,u)+ g(x),\quad x\in {\mathbb {R}}^N, \end{aligned}$$ M ∫ ∫ R 2 N | u...
In this paper, we present some Lyapunov-type inequalities for a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. As an application, we obtain a lower bound for the eigenvalues of corresponding equations.
In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for a class of problem for nonlinear implicit fractional differential equations (IFDE for short) with Hadamard fractional derivative. We present two examples to show the applicability of our results.
In this paper, we propose some fixed point results for a new type of contractive multivalued operators in the setting of $$\mathcal {H}^+$$ H + -metric spaces which are further applied to get results on data dependence and well-posed multivalued problems. By doing this, our work generalizes Nadler’s, Kikkawa and Suzuki’s, and some other fixed point theorems. The theorems provided allow...
Let E be a commutative unital Banach algebra, X a compact Hausdorff space, and $$ \mathcal {A} \subset C(X,E)$$ A ⊂ C ( X , E ) a Banach E-valued function algebra. An E-valued spectrum $$E{\text {-}}{\textsc {sp}}(f)$$ E - S P ( f ) of every $$f\in \mathcal {A} $$ f ∈ A is introduced and investigated, and it is shown that $$E{\text {-}}{\textsc {sp}}(f)$$...
Our interest in this paper is to prove strong convergence results for finding zeros of the sum of two accretive operators by utilizing a viscosity type forward–backward splitting method. We also discuss applications of this method to approximation of solution to certain integro-differential equation with generalized p-Laplacian operator. Our results complement many recent and important results in...
Our aim in this article is to study the long time behavior, in terms of finite dimensional attractors, of a class of doubly nonlinear Allen–Cahn equations with singular potentials. In particular, we prove the existence of the global attractor which has finite fractal dimension.
We establish uniqueness of the solution of the unsteady state dam problem in the heterogeneous and rectangular case assuming the dam wet at the bottom and dry near to the top.
We study splittability over some classes of compact spaces which are useful in functional analysis and general topology. Among other things we show that a scattered pseudocompact space splittable over the class of Eberlein compact spaces is Eberlein compact. We also prove that a compact space splittable over the class of Eberlein compact spaces is hereditarily $$\sigma $$ σ -metacompact,...
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