Radical classes of l-groups by Dao-Rong Ton

“…In the sections 5-6 we give nice concrete descriptions of some important radical classes of l-groups using the structure theorems of a complete l-group and an Archimedean l-group.…”
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Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces by Aneta Sikorska-Nowak

“…We prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0)=x0, t∈Ia=[0,a], a>0, where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of HL. …”
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New Expansion Formulas for a Family of the λ-Generalized Hurwitz-Lerch Zeta Functions by H. M. Srivastava, Sébastien Gaboury

“…These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. …”
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Generalization of some absolute summability methods by W. T. Sulaiman

“…Mazhar (1971) gave the characterization for the series ∑anϵn to be summable |N,pn| whenever ∑an is summable |C,α|k, α≥0, k≥1. Here we prove two theorems, the first concerns the sufficient conditions and the second the necessary conditions satisfied by {ϵn} in order to have ∑anϵn summable |N¯,pn|k whenever ∑an is summable |C,α|k, k≥1.…”
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The n-dimensional distributional Mellin transformation by Sunil Kumar Sinha

“…The n-dimensional distributional Mellin transformation is developed using the testing function space Mc,d and its dual M′c,d The standard theorems on analyticity, uniqueness and continuity are proved. …”
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Positive Solutions for Singular Complementary Lidstone Boundary Value Problems by Fanglei Wang, Yukun An

“…By using fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: (−1)𝑛𝑢(2𝑛+1)(𝑡)=ℎ(𝑡)𝑓(𝑢(𝑡)), in 0<𝑡<1, 𝑢(0)=0, 𝑢(2𝑖+1)(0)=𝑢(2𝑖+1)(1)=0, 0≤𝑖≤𝑛−1, where 𝑛∈𝑁.…”
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Some Properties of Certain Multivalent Analytic Functions Involving the Cătas Operator by E. A. Elrifai, H. E. Darwish, A. R. Ahmed

“…Such results as subordination and superordination properties, convolution properties, inclusion relationships, distortion theorems, inequality properties, and sufficient conditions for multivalent starlikeness are provide. …”
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Dirichlet and Neumann Problems Related to Nonlinear Elliptic Systems: Solvability, Multiple Solutions, Solutions with Positive Components by Luisa Toscano, Speranza Toscano

“…We study the solvability of Dirichlet and Neumann problems for different classes of nonlinear elliptic systems depending on parameters and with nonmonotone operators, using existence theorems related to a general system of variational equations in a reflexive Banach space. …”
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Optimal $L^2$ Extensions of Openness Type and Related Topics by Xu, Wang, Zhou, Xiangyu

“…We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. …”
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Finite volume schemes and Lax–Wendroff consistency by Eymard, Robert, Gallouët, Thierry, Herbin, Raphaele, Latché, Jean-Claude

“…We present a (partial) historical summary of the mathematical analysis of finite difference and finite volume methods, paying special attention to the Lax–Richtmyer and Lax–Wendroff theorems. We then state a Lax–Wendroff consistency result for convection operators on staggered grids (often used in fluid flow simulations), which illustrates a recent generalization of the flux consistency notion designed to cope with general discrete functions.…”
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On Multivalued Hybrid Contractions with Applications by Monairah Alansari, Shehu Shagari Mohammed, Akbar Azam, Nawab Hussain

“…Nontrivial examples are also provided to support the assertions of our theorems.…”
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Existence and Uniqueness of Positive Solutions for a Coupled System of Fractional Differential Equations by Hanying Feng, Xiaofeng Zhang

“…Firstly, we give Green’s functions and prove their properties; secondly, the existence and uniqueness of positive solutions are obtained by using some fixed point theorems. In addition, two examples are presented to demonstrate the application of our main results.…”
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Some Generalized Formulas of Hadamard-Type Fractional Integral Inequalities by Xiujun Zhang, Ghulam Farid, Hafsa Yasmeen, Kamsing Nonlaopon

“…Refinements of well-known inequalities are also deducible from the established theorems.…”
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On Neutrosophic 2-Metric Spaces with Application by Ali Asghar, Aftab Hussain, Khaleel Ahmad, Umar Ishtiaq, Hamed Al Sulami, Nawab Hussain

“…In this situation, we prove various fixed point theorems. The findings support previous methodologies in the literature and are backed up by various examples and an application.…”
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Solving Advection Equations by Applying the Crank-Nicolson Scheme Combined with the Richardson Extrapolation by Zahari Zlatev, Ivan Dimov, István Faragó, Krassimir Georgiev, Ágnes Havasi, Tzvetan Ostromsky

“…The accuracy of the numerical solution can sometimes be increased substantially by applying the Richardson Extrapolation. Two theorems related to the accuracy of the calculations will be formulated and proved in this paper. …”
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A new approach for the bigeometric newton method by Numan Yalçın, Ercan Celık

“…For this, the basic definitions and theorems of bigeometric analysis, which is one of the non-Newtonian analysis, were used. …”
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Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations by Tongxing Li, Yuriy V. Rogovchenko

“…We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. …”
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On some new N-independent-variable discrete inequalities of the Gronwall type by En Hao Yang

“…Their consequence for the case of N=3, generalizes all of the known theorems obtained by Pachpatte and Singare in [1]. …”
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Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces by Shenghua Wang, Shin Min Kang

“…Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.…”
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Existence and Ulam–Hyers stability results for Caputo–Hadamard fractional differential equations with non-instantaneous impulses by Mesfin Teshome Beyene, Mitiku Daba Firdi, Tamirat Temesgen Dufera

“…By employing Banach’s and Schaefer’s fixed-point theorems, we attain the required results. Finally, we provide examples that support the main findings we arrived at.…”
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