Generalized m-Polar Fuzzy Positive Implicative Ideals of BCK-Algebras by Anas Al-Masarwah, Abd Ghafur Ahmad, G. Muhiuddin, D. Al-Kadi

“…Several properties, examples, and characterization theorems of these concepts are considered.…”
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Polynomial time algorithm for solving k-coverage problem in wireless sensor networks by Qi WANG, Zheng’an XIAO, Huaixing WANG

“…How to solve the k-coverage problem,which was divided into worst-case and best-case,inside the two-dimensional target area in wireless sensor networks was explored,and a polynomial time algorithm for solving this problem was put forward.In this algorithm,a series of definitions and theorems were proposed based on the geometric graph of growing disks,and the k-coverage problem was transformed into one of finding a series of adjacent borders.The simulation results show that the algorithm could compute the optimal k-breach path and k-support path in polynomial time,so as to avoid or select the network coverage reasonably.…”
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The Existence and Uniqueness of a Class of Fractional Differential Equations by Zhanbing Bai, Sujing Sun, YangQuan Chen

“…By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D0+qx(t)=f(t,x(t),  D0+q-1x(t)),  t∈(0,T),  x(0)=0,  D0+q-1x(0)=x0,  are discussed, where f∈C([0,T]×R2,R),D0+qx(t) is the standard Riemann-Liouville fractional derivative, 1<q<2. …”
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Generalized roughness of three dimensional ( $$\in ,\in \vee q$$ ∈ , ∈ ∨ q )-fuzzy ideals in terms of set-valued homomorphism by Shahida Bashir, Rabia Mazhar, Nasreen Kausar, Saziye Yaman, Syed Suleman Ali, Muneeb Ul Hassan Afzal

“…Abstract The objective of this study is to generalize the roughness of a fuzzy set-in three-dimensional structure by introducing ternary multiplication. Many results and theorems of rough fuzzy ideals have been extended from semigroup and semiring, to ternary semiring by introducing the definition of a rough fuzzy subset of ternary semiring. …”
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Coupled and Tripled Coincidence Point Results with Application to Fredholm Integral Equations by Marwan Amin Kutbi, Nawab Hussain, Jamal Rezaei Roshan, Vahid Parvaneh

“…The aim of this paper is to define weak α-ψ-φ-contractive mappings and to establish coupled and tripled coincidence point theorems for such mappings defined on Gb-metric spaces using the concept of rectangular G-α-admissibility. …”
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Iterative Scheme with Errors for Common Zeros of Finite Accretive Mappings and Nonlinear Elliptic Systems by Li Wei, Ruilin Tan

“…We present a new iterative scheme with errors to solve the problems of finding common zeros of finite m-accretive mappings in a real Banach space. Strong convergence theorems are established, which extend the corresponding works given by some authors. …”
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Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales by Chengjun Yuan, Yongming Liu

“…The arguments are based upon fixed-point theorems in a cone.…”
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Finite-part singular integral approximations in Hilbert spaces by E. G. Ladopoulos, G. Tsamasphyros, V. A. Zisis

“…Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. …”
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Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces by Abhimanyu Kumar, Dharmendra K. Gupta, Eulalia Martínez, Sukhjit Singh

“…The region of accessibility and a way to enlarge the convergence domain are provided. Theorems are given for the existence-uniqueness balls enclosing the unique solution. …”
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Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices by Gashaye Dessalew, Tesfaye Kebede, Gurju Awgichew, Assaye Walelign

“…Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. …”
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Soft Congruence Relations over Rings by Xiaolong Xin, Wenting Li

“…In particular, the first, second, and third soft isomorphism theorems are established, respectively.…”
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Notes on Upper and Lower Truncation of Picture Fuzzy Graphs by Muhammad Shoaib, Waqas Mahmood, Ahmad N. Al-Kenani, Sahidul Islam

“…The degree of an edge in both Up-T and Low-T of Pic-FG is discussed. Some related theorems related to the degree of Up-T and Low-T of Pic-FG are discussed.…”
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Strictly barrelled disks in inductive limits of quasi-(LB)-spaces by Carlos Bosch, Thomas E. Gilsdorf

“…Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi-(LB)-space is bounded. …”
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Exploring the Structure of Possibility Multi-Fuzzy Soft Ordered Semigroups Through Interior Ideals by Sana Habib, Kashif Habib, Violeta Leoreanu-Fotea, Faiz Muhammad Khan

“…Various results, formulated as theorems based on these concepts, are presented and further validated with suitable examples. …”
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On q-Rung Orthopair Fuzzy Subgroups by Asima Razzaque, Abdul Razaq

“…We also present q-rung orthopair fuzzy coset and q-rung orthopair fuzzy normal subgroup along with relevant fundamental theorems. Moreover, we introduce the concept of q-rung orthopair fuzzy level subgroup and proved related results. …”
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Noether symmetry of multi-delay Birkhoffian system and its conserved quantity by Xin-Yu Du, Xiang-Hua Zhai

“…Third, due to the effects of different time delays, the corresponding Noether-type theorems of multi-delay Birkhoffian systems are obtained. …”
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Dirichlet type extensions of Euler sums by Xu, Ce, Wang, Weiping

“…By using the method of residue computations, we establish the explicit formulas for the (alternating) linear and quadratic Euler $T$-sums and $\tilde{S}$-sums, from which, the parity theorems of Hoffman’s double and triple $t$-values and Kaneko–Tsumura’s double and triple $T$-values are further obtained. …”
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A continuous-time network evolution model describing $ N $-interactions by István Fazekas, Attila Barta, László Fórián, Bettina Porvázsnyik

“…The basic properties of the evolution process were described. Asymptotic theorems were proved for the number of cliques having a fixed size and the degree of a fixed node. …”
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Present value of firm in case of correlated defaults by Mantas Valužis

“…Also, the modelling of other financial risks, notably, the market risk (the change of debt value) and the operational risk (the adequacy of selected credibility criteria) are included in these theorems. Using the principle of conservatism in credit risk assessment, the debtor credibility, the debt value and the firm value are assumed to follow geometric Wiener process. …”
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A New Iterative Scheme for Generalized Mixed Equilibrium, Variational Inequality Problems, and a Zero Point of Maximal Monotone Operators by Kriengsak Wattanawitoon, Poom Kumam

“…Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. …”
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