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In the paper, the spectra of weighted composition operators on Hardy-type spaces of holomorphic functions on the unit disc of the complex plane are studied. The spectra of invertible operators induced by elliptic and parabolic automorphisms are described, for weighted composition operators acting on abstract Hardy spaces generated by Banach lattices. We also study spectra of weighted composition operators...
Some new refinements of Hermite–Hadamard type inequalities are obtained. These results involve some different types of fractional integrals. Special cases which are naturally included in the main results of the paper are also discussed.
In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of differential equations. Concretely speaking, the authors find four explicit formulas for these polynomials and for derivatives of generating functions of these polynomials, establish four identities between these two kinds of polynomials, and significantly simplify some known results.
A new class $$K_p(\alpha ,\beta )$$ K p ( α , β ) consisting of the functions which are p-valent close-to-convex of order $$\beta $$ β and type $$\alpha $$ α is introduced. The object of the present paper is to derive some sufficient conditions for functions to be in the class $$K_p(\alpha ,\beta )$$ K p ( α , β ) .
In this article, we establish the existence of solution of infinite systems of integral equations in two variables in the sequence space $$\ell _{p}(1<p<\infty )$$ ℓ p ( 1 < p < ∞ ) by using Meir–Keeler condensing operators. We explain the results with the help of simple examples.
We study a weaker and more natural notion of stability called weak $$w^{2}$$ w 2 -stability to get an insight in the corresponding results obtained by Măruşter and Măruşter (J Comput Appl Math 276:110–116, 2015) and Wang (J Comput Appl Math 285:226–229, 2015). A data dependence result for fixed points of strongly demicontractive operators is also established. Some illustrative examples are...
We extend the splitting theory for $$\hbox {PLS}$$ PLS spaces and the corresponding parameter dependence problem to the context of hilbertizable spaces. In particular, we characterize for fixed $$\hbox {PLH}$$ PLH spaces E and X, i.e. strongly reduced projective limits of inductive limits of Hilbert spaces, the splitting of each short exact sequence $$\begin{aligned} 0 \rightarrow X \xrightarrow...
The main purpose of this paper is using the analytic methods and a relation between the two-term cubic exponential sums and general Kloosterman sums to study the computational problem of one kind high-th power mean of general Kloosterman sums for some special non-principal character $$\chi \bmod p$$ χ mod p , and give four exact computational formulae for them. As applications of these results,...
We study the (possible) relation between diameter two properties and various notions of polyhedrality. I-polyhedral spaces (being non-reflexive, M-embedded) have the strong diameter two property; however it turns out that even in II-polyhedral spaces the unit ball may contain slices of small diameter.
Let $$\mathcal {P}$$ P be the family of all proximinal subsets of a Banach space X. Let $$P:(X,\mathcal {P})\rightarrow 2^{X}$$ P : ( X , P ) → 2 X be the generalized metric projection defined as $$P(x,A)=P_{A}(x)=\{a\in A:\Vert x-a\Vert =d(x,A)\}$$ P ( x , A ) = P A ( x ) = { a ∈ A : ‖ x - a ‖ = d ( x , A ) } for any $$(x,A)\in (X,\mathcal {P})$$ ( x , A )...
In this note, we point out that several assertions (Proposition 7, Lemmas 20, 21 and Theorems 7, 15) in [Y. Shao and K. Qin, Fuzzy soft sets and fuzzy soft lattices, Int. J. Comput. Intell. Sys. 5 (2012), 1135–1147] are not true in general. Appropriate counterexamples are given. Further their modified versions are presented.
In this paper, we prove some new inequalities of Levinson-type on time scales. Also we will prove some new extensions of these inequalities via convexity.
In this article, we study a generalized variational inequality problem with multi-valued mappings over product sets and the system of generalized variational inequalities with multi-valued mappings which are equivalent problems. By developing the idea of generalized densely relatively pseudomonotone mappings, and by using well-known Fan-KKM theorem and fixed point theorem, we prove existence results...
This paper is a continuation of the work done by Deo et al. (Appl. Math. Comput. 273, 281–289, 2016), in which the authors have established some approximation properties of the Stancu–Kantorovich operators based on Pólya–Eggenberger distribution. We obtain some direct results for these operators by means of the Lipschitz class function, the modulus of continuity and the weighted space. Also, we study...
Let f be the function defined on the open unit disk, with $$f(0)=0=f'(0)-1$$ f ( 0 ) = 0 = f ′ ( 0 ) - 1 , satisfying the subordinations $$zf'(z)/f(z)\prec \alpha + (1-\alpha )e^{z}$$ z f ′ ( z ) / f ( z ) ≺ α + ( 1 - α ) e z or $$zf'(z)/f(z)\prec \alpha + (1-\alpha )\sqrt{1+ z}$$ z f ′ ( z ) / f ( z ) ≺ α + ( 1 - α ) 1 + z respectively, where $$0\le...
We focus on the improvements for Young inequality. We give elementary proof for known results by Dragomir, and we give remarkable notes and some comparisons. Finally, we give new inequalities which are extensions and improvements for the inequalities shown by Dragomir.
We give the necessary and/or sufficient conditions for the multiplication operators between two vector valued sequence spaces to be mixing. As a consequence of some general results we find the necessary and sufficient condition for the multiplication operator $$M_{\mathcal {V}}:c_{0}\left( \mathcal {X}\right) \rightarrow c_{0}\left( \mathcal {Y}\right) $$ M V : c 0 X → c 0 Y (respectively...
In this paper two new subclasses of p-valent starlike functions are introduced and investigated. Inclusion relations, integral transforms, distortion bounds and convolution properties for each of these p-valent function classes are obtained.
In this paper, a fixed method is introduced and investigated for solving a split feasibility problem. A strong convergence theorem of solutions is established in the framework of infinite dimensional Hilbert spaces. As an application, a split equality problem is also investigated.
The aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class representative on the set of the k-letter alphabet. By using the unified zeta-type function and the unification of the Apostol-type numbers which are defined by Ozden et al. (Comput Math Appl 60:2779–2787, 2010), we give an alternating series for the...
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