Complete Solutions to General Box-Constrained Global Optimization Problems by Dan Wu, Youlin Shang

“…Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. …”
Get full text

Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter by Elgiz Bairamov, M. Seyyit Seyyidoglu

“…In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of 𝐴. …”
Get full text

Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators by D. L. Suthar, Fasil Gidaf, Mitku Andualem

“…The aim of this study is to introduce new (presumed) generalized fractional integral operators involving I-function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized M-series and also to study the different properties of the generalized M-series. …”
Get full text

Exploring the 2-Part of Class Groups in Quadratic Fields: Perspectives on the Cohen–Lenstra Conjectures by Yong Wang, Huili Zhang, Ying Zhou, Haopeng Deng, Lingyue Li

“…We provide detailed proofs of key theorems related to ideal decompositions and modular homomorphisms, and we explore the distribution of class groups of imaginary quadratic fields. …”
Get full text

Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems by Lu-Chuan Ceng, Juei-Ling Ho

“…We prove some strong and weak convergence theorems for the proposed iterative algorithms under mild conditions.…”
Get full text

The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces by Rabian Wangkeeree

“…We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. …”
Get full text

A New Iterative Method for Equilibrium Problems and Fixed Point Problems by Abdul Latif, Mohammad Eslamian

“…We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. …”
Get full text

Sufficient and Necessary Conditions of Complete Convergence for Weighted Sums of PNQD Random Variables by Qunying Wu

“…Our results generalize and improve those on complete convergence theorems previously obtained by Baum and Katz (1965) and Wu (2002).…”
Get full text

Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features by H. Salah, M. Anis, C. Cesarano, S. S. Askar, A. M. Alshamrani, E. M. Elabbasy

“…Lastly, we provide examples and review previous theorems from the literature to compare our findings.…”
Get full text

Existence of a unique solution to a fourth-order boundary value problem and elastic beam analysis by Ravindra Rao, Jagan Mohan Jonnalagadda

“…The primary tools employed in this study include the application of Banach's and Rus's fixed point theorems. Our theoretical results are applied to elastic beam deflections when the beam is subjected to a loading force and both ends are clamped. …”
Get full text

SIMULATION OF THE ELECTROSTATIC DIPOLE FIELD IN THE PRESENCE OF A THIN UNCLOSED OBLATE ELLIPSOIDAL SHELL AND PLANE by G. Ch. Shushkevich

“…An analytical solution of axially symmetric problem for determining the field of an electrostatic dipole located inside a thin unclosed oblate ellipsoidal shell in the presence of a grounded plane is constructed. Using the addition theorems connecting spherical, ellipsoidal and cylindrical harmonic functions, the solution of the boundary problem is reduced to the solution of dual series equations by the Legendre polynomials that are transformed to an infinite system of linear algebraic equations of the second kind with a completely continuous operator. …”
Get full text

Non-Archimedean valued quasi-invariant descending at infinity measures by S. V. Lüdkovsky

“…Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. …”
Get full text

The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence by Linxin Li, Dingping Wu

“…Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. …”
Get full text

Asymptotic Distributions for Power Variations of the Solution to the Spatially Colored Stochastic Heat Equation by Wensheng Wang, Xiaoying Chang, Wang Liao

“…We use the underlying explicit kernels and spectral/harmonic analysis, yielding temporal central limit theorems for SHEs with spatially colored noise. This work builds on the recent works on delicate analysis of variations of general Gaussian processes and SHEs driven by space-time white noise.…”
Get full text

A Complete Normed Space of a Class of Guage Integrable Functions by Yassin Alzubaidi

“…This result opens the gate for further studies, such as investigating the verity of convergence theorems on the presented space and studying its other properties.…”
Get full text

Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse by Rauf Kh. Amırov, A. Adiloglu Nabıev

“…Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.…”
Get full text

Fixed-Point Results Related to b-Intuitionistic Fuzzy Metric Space by Mohamed Altanji, Annamalai Santhi, Vediyappan Govindan, Shyam Sundar Santra, Samad Noeiaghdam

“…Subsequently, we simplify the proofs of manifold fixed-point theorems in the intuitionistic fuzzy b-metric spaces under the prominent contraction conditions. …”
Get full text

New Inner Product Quasilinear Spaces on Interval Numbers by Hacer Bozkurt, Yılmaz Yilmaz

“…Primarily we examine the new example of quasilinear spaces, namely, “IRn interval space.” We obtain some new theorems and results related to this new quasilinear space. …”
Get full text

Generalized Lebesgue Points for Hajłasz Functions by Toni Heikkinen

“…As an application we obtain Lebesgue type theorems for Lorentz–Hajłasz, Orlicz–Hajłasz, and variable exponent Hajłasz functions.…”
Get full text

An Approach of Integral Equations in Complex-Valued b-Metric Space Using Commuting Self-Maps by Rashad A. R. Bantan, Saif Ur Rehman, Shahid Mehmood, Waleed Almutiry, Amani Abdullah Alahmadi, Mohammed Elgarhy

“…This paper is aimed at establishing some unique common fixed point theorems in complex-valued b-metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. …”
Get full text