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The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to p -absolutely summable spaces are a new concept that is introduced in this article. We look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces. [ABSTRACT FROM AUTHOR]

In this work, we introduce weak Pata convex contractions and weak E -Pata convex contractions via simulation functions in metric spaces to prove some fixed point results for such mappings. Also, we consider an example related to weak Pata convex contractions. Consequently, our results generalize and unify some results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we mainly obtain an approximation theorem and generic convergence of solutions for inverse quasivariational inequality problems. First, we define the concept of the approximate solution to inverse quasivariational inequality problems under bounded rationality theory. Afterward, an approximation theorem that satisfies fairly mild assumptions is proved. Moreover, we establish a function space and discuss the convergence properties of solutions for inverse quasivariational inequality problems by the method of set-valued analysis. Finally, we prove that most of inverse quasivariational inequality problems are stable in the case of perturbation of the objective function. These results are new, which improve the corresponding outcomes of the recent literatures. [ABSTRACT FROM AUTHOR]

In this paper, we construct and investigate the space of weighted Gamma matrix of order r in Nakano sequence space of soft functions. The idealization of the mappings has been achieved through the use of extended s -soft functions and this sequence space of soft functions. This new space's topological and geometric properties, the multiplication mappings that stand in on it, and the mappings' ideal that correspond to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated prequasi ideal. Interestingly, several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of nonlinear difference equations of soft functions are introduced. [ABSTRACT FROM AUTHOR]

In general, we have constructed the operator ideal generated by extended s -fuzzy numbers and a certain space of sequences of fuzzy numbers. An investigation into the conditions sufficient for variable exponent Cesàro sequence space of fuzzy functions furnished with the definite function to create pre-quasi-Banach and closed is carried out. The R and the normal structural properties of this space are shown. Fixed points for Kannan contraction and nonexpansive mapping have been introduced. Lastly, we explore whether the Kannan contraction mapping has a fixed point in its associated pre-quasioperator ideal. The existence of solutions to nonlinear difference equations is illustrated with a few real-world examples and applications. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the long-time behavior of g -Navier-Stokes equations with weak dampnesss and time delay. The uniformly attracting sets of processes are obtained. On the basis of the method with asymptotic compactness, the existence of the uniform attractor for the equation is proved with the restriction of the forcing term belonging to translational compacted function space. [ABSTRACT FROM AUTHOR]

A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce and study several types of Kakeya inequalities by the maximal functions in Hardy spaces in ℝ n , n ≥ 2 , and we could obtain several inequalities associated with the Kakeya inequalities. We will show that M δ S α , β t f p ≲ p , n , φ , ε 1 / δ 5 n / r + 2 ε f p , when f x ∈ L p ℝ n and supp f ^ ξ ⊆ B 0 , 1 . [ABSTRACT FROM AUTHOR]

The space of fractional Cauchy transforms plays a central role in classical complex analysis, harmonic analysis, and geometric measure theory. In this paper, we study the boundedness and compactness of product-type operators from the space of fractional Cauchy transforms to the Zygmund-type space in terms of the function theoretic characterization of Julia–Carathéodory type. [ABSTRACT FROM AUTHOR]

We have defined the variable exponent of the Cesàro complex function space of formal power series. We have constructed the prequasi-ideal generated by s -numbers and this new space of complex functions. We present some topological and geometric structures of this class of ideal. The existence of Caristi's fixed point is examined. Some geometric properties related to the fixed point theory are presented. Finally, real-world examples and applications show solutions to some nonlinear difference equations. [ABSTRACT FROM AUTHOR]

Let X , d , μ be a metric measure space endowed with a metric d and a non-negative Borel doubling measure μ. Let L be a non-negative self-adjoint operator on L 2 X . Assume that the (heat) kernel associated to the semigroup e − t L satisfies a Gaussian upper bound. In this paper, we prove that the Musielak–Orlicz–Hardy space H φ , L X associated with L in terms of the Lusin-area function and the Musielak–Orlicz–Hardy space H L , G , φ X associated with L in terms of the Littlewood–Paley function coincide and their norms are equivalent. To do this, we first establish the discrete characterization of these two spaces. It improves the known results in the literature. [ABSTRACT FROM AUTHOR]

We have defined and studied the weighted Nakano sequence spaces of fuzzy functions. We have constructed the ideal generated by extended s -fuzzy functions and the sequence spaces of fuzzy functions. We present some topological and geometric structures of this class of ideal and multiplication mappings acting on this sequence space of fuzzy functions. Moreover, the existence of Caristi's fixed point is examined. To show how the work is done, some examples and applications to the existence of solutions for a class of nonlinear summable and matrix equations are also talked about. [ABSTRACT FROM AUTHOR]

The space of fractional Cauchy transforms plays a central role in classical complex analysis, harmonic analysis, and geometric measure theory. In this paper, we study the boundedness and compactness of product-type operators from the space of fractional Cauchy transforms to the Zygmund-type space in terms of the function theoretic characterization of Julia–Carathéodory type. [ABSTRACT FROM AUTHOR]

This paper establishes the reality of a fixed point of Kannan's prequasinorm contraction mapping on the variable exponent function space of complex variables, demonstrating that it satisfies the property (R) and possesses a prequasinormal structure. We have established the presence of a fixed point of Kannan prequasinorm nonexpansive mapping on it and Kannan prequasinorm contraction mapping in the prequasi-Banach operator ideal, created by this function space and s -numbers. Finally, we provide some applications for solutions to summable equations and illustrate instances to corroborate our findings. [ABSTRACT FROM AUTHOR]

Using some new techniques, the necessary and sufficient conditions for Kadec-Klee property of Orlicz function spaces equipped with s-norms are presented. An original method that was used in the process of inquiry and the obtained results also systematically complete and broaden the characterization of Kadec-Klee property of Orlicz spaces. [ABSTRACT FROM AUTHOR]

Let θ ≥ 0 and p · be a variable exponent, and we introduce a new class of function spaces L p · , θ in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with θ = 0 and grand Lebesgue spaces with p · ≡ p and θ = 1. Based on the new spaces, we introduce a kind of Hardy-type spaces, grand martingale Hardy spaces with variable exponents, via the martingale operators. The atomic decompositions and John-Nirenberg theorem shall be discussed in these new Hardy spaces. [ABSTRACT FROM AUTHOR]

The article titled "Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model" has been retracted by Hindawi, the publisher, due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, and availability of data, as well as inappropriate citations and incoherent content. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Neutrosophic Extension of the Maxwell Model: Properties and Applications" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that their usual quality checks did not identify these issues before publication and has implemented additional measures to safeguard research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: A New Extension of the Exponentiated Weibull Model Mathematical Properties and Modelling" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Positive Weighted Symmetry Function Kernels and Some Related Inequalities for a Generalized Class of Convex Functions" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Notion of Complex Spherical Fuzzy Graph with Application" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Approximations of Intuitionistic Fuzzy Ideals over Dual Spaces by Soft Binary Relations" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Applications of Hesitant Interval Neutrosophic Linguistic Schweizer-Sklar Power Aggregation Operators to MADM" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Applications of Karry-Kalim-Adnan Transformation (KKAT) to Mechanics and Electrical Circuits" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Multiplicative Topological Properties on Degree Based for Fourth Type of Hex-Derived Networks" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Development of Neutrosophic Cubic Graphs with Applications in Decision Sciences" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Degree-Based Graph Invariants of some Chemical Structures for the Treatment of Corona Virus" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Analysis of Fuzzy Kuramoto-Sivashinsky Equations under a Generalized Fuzzy Fractional Derivative Operator" has been retracted by Hindawi, the publisher, due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content, and readers are advised that it is unreliable. Wiley and Hindawi have implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Global Exponential Stability of Both Continuous-Time and Discrete-Time Switched Positive Time-Varying Delay Systems with Interval Uncertainties and All Unstable Subsystems" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and manipulated peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Study of Neighborhood Degree-Based Topological Indices via Direct and NM-Polynomial of Starphene Graph" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Roughness in Hypervector Spaces" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to safeguard research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Adjacency Metric Dimension of Some Families of Graph" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and manipulated peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to safeguard research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

In this article, we introduce and study a new class of operators defined on a Cartesian product of ideal spaces of measurable functions. We use the general approach of the theory of vector lattices. We say that an operator T : E × F ⟶ W defined on a Cartesian product of vector lattices E and F and taking values in a vector lattice W is orthogonally biadditive if all partial operators T y : E ⟶ W and T x : F ⟶ W are orthogonally additive. In the first part of the article, we prove that, under some mild conditions, a vector space of all regular orthogonally biadditive operators O B A r E , F ; W is a Dedekind complete vector lattice. We show that the set of all horizontally-to-order continuous regular orthogonally biadditive operators is a projection band in O B A r E , F ; W . In the last section of the paper, we investigate orthogonally biadditive operators on a Cartesian product of ideal spaces of measurable functions. We show that an integral Uryson operator which depends on two functional variables is orthogonally biadditive and obtain a criterion of the regularity of an orthogonally biadditive Uryson operator. [ABSTRACT FROM AUTHOR]

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions. [ABSTRACT FROM AUTHOR]

In this article, we define a kind of truncated maximal function on the Heisenberg space by M γ c f x = sup 0 < r < γ 1 / m B x , r ∫ B x , r f y d y. The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1 < p < ∞ , the L p norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p = 1 , we get the equivalence of weak norm L 1 ⟶ L 1 , ∞ and M ̇ 1 , λ ⟶ W ̇ M 1 , λ . Those results are generalization of previous work on Euclid spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in the proof. The admissibility of the function space topology and KKM-Theorem have played important role in proving the results. [ABSTRACT FROM AUTHOR]

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space. [ABSTRACT FROM AUTHOR]

All entire functions which transform a class of holomorphic Zygmund-type spaces into weighted analytic Bloch space using the so-called n -generalized superposition operator are characterized in this paper. Moreover, certain specific properties such as boundedness and compactness of the newly defined class of generalized integral superposition operators are discussed and established by using the concerned entire functions. [ABSTRACT FROM AUTHOR]

In this paper, we prove by means of a fixed-point theorem an existence result of the Cauchy problem associated to an ordinary differential equation in modular function spaces endowed with a reflexive convex digraph. [ABSTRACT FROM AUTHOR]

Let X be a ball Banach function space on ℝ n . We introduce the class of weights A X ℝ n . Assuming that the Hardy-Littlewood maximal function M is bounded on X and X ′ , we obtain that BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A X ℝ n . As a consequence, we have BMO ℝ n = α ln ω : α ≥ 0 , ω ∈ A L p · ℝ n ℝ n , where L p · ℝ n is the variable exponent Lebesgue space. As an application, if a linear operator T is bounded on the weighted ball Banach function space X ω for any ω ∈ A X ℝ n , then the commutator b , T is bounded on X with b ∈ BMO ℝ n . [ABSTRACT FROM AUTHOR]

This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity. [Extracted from the article]

We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. [Extracted from the article]

This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. [Extracted from the article]

This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. [Extracted from the article]

Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity. This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. [Extracted from the article]

We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. [Extracted from the article]

This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity. [Extracted from the article]

This article has been retracted by Hindawi following an investigation undertaken by the publisher [[1]]. We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation. Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity. [Extracted from the article]